Medicine for the Sky

Compass and Straightedge geometry meets HTML5

2012-05-18T23:05:00.000-04:00

This is a proof of concept build of an HTML5 engine to perform classical Greek compass and straightedge calculations, as described in this Wikipedia article. In brief, an initial set of points can be created, and then points can be connected by lines, circles can be drawn with one point as center and another as one point in the circumference, and finally the points where circles and/or lines intersect can be added as new points. With those simple rules, angles and line segments can be bisected, and certain regular (equilateral) shapes can be created.

I have created a rudimentary language to describe the adding of points, lines, and circles, and finding their intersections, which I discuss briefly after the demo below. Without further ado, choose a sample "program" to run to bisect an angle or create a regular shape. If you're a fan of Gauss, be sure to check out the heptadecagon.

Display area

Frame delay (ms)

Samples
Bisect an angle
Construct a regular triangle
Pentagon
Heptadecagon
Instructions

The language

point [x] [y] [name]
This creates a point at canvas position [x,y], and labels it [name]. This is intended only to be used for creating starting points to be used by the remaining commands. In HTML5 canvases, point 0,0 is the upper-left corner, and numbers increase as you move right and down.
line [a] [b]
This draws a line between points a and b.
circle [a] [b]
This draws a circle centered at point a, with point b as a point on the circumference (line ab describes the circle's radius)
intersect [circle|line] [a] [b] [circle|line] [c] [d]
Identify's the intersection points between two circles, two lines, or a circle and a line (for this last combination, specify the circle first). This doesn't add any new points, it just identifies the intersections. A separate "point" command must follow an intersect command to add new points
point i [0|1] [a]
This creates a new point [a] based on the two possible results of the last "intersect" command. You will need to test whether intersect point 0 or 1 is the one you need. In fact, if you're building your own program, you'll want to do several tests as you go. I recommend setting the frame delay to 0 before testing to speed things up.
: [text]
Sets the current "label" in the display area, used for giving the audience an idea about what they're looking at.
# [comment]
Comments in the instructions that aren't shown in the display area

Enjoy!

Animated prime number machine

2012-05-10T21:32:00.000-04:00

This uses the HTML5 canvas architecture, so no IE8 or less; sorry. I have only tested it with Google Chrome, so it may not work in other HTML5-capable browsers. If you find this to be the case, please leave feedback with any errors you see, and what browser version you're using, and I'll see what I can do to get it working for you.

The principle of the prime number machine is of rolling coins and elevators. I created this because I thought it would be neat to have a way for prime numbers to be produced by a set of mechanical rules rather than with pure mathematical methods. Here is a basic description of the rules:

If a coin rolls into an empty box, it creates an elevator with the height shown on the coin, and a new empty box appears.
If a coin hits the top or bottom of an existing elevator, it bounces off with no effect.
The coin's number increments after each cycle
The elevators go down a floor during each cycle until the top car is flush with the ground line, then they begin going back up to where they started.

This results in two basic phenomena: All new elevators correspond to prime numbers. When a coin does not have a prime number on it, all of the elevators corresponding to the coin's prime factors have a car flush with the ground.

Enjoy!

Encounters with the police

2011-12-07T17:27:00.000-05:00

The cops have had an awful lot of bad press lately, for example the interactions with OWS protestors such as this one, and this sobering article from the Sarasota Herald-Tribune, or this report of a former marine killed in his home by a SWAT team who erroneously thought he was a drug dealer. And erroneously thought their team member who tripped had just been shot.

My personal encounters with law enforcement have been qualitatively different. I have interacted with the police 26 times, and although that number seems large, none of them ended in an arrest, and in only two seemed like good material for an episode of Cops. In rough order of occurrence (I'm approximating my age on a few of these), they are:

1. When I was about 13, I was on a canoe trip where a boy drowned, and the police were called to investigate. A friend of the victim broke down crying at one point, and the officer taking the report was very consoling to her.

2. At 15, my bicycle was stolen. My stepfather called the police, an officer came to our apartment to take a report. Our apartment smelled of weed most of the time, as my folks smoked quite a bit of it. The officer either didn't notice, or didn't mention it. He took the report, informed us that it's rare to make a recovery, but they would nonetheless give it the ol' college try.

3. At 16, a pair of officers knocked on our open apartment door late one night when we were sleeping, to verify we weren't being robbed. I assume a neighbor saw the door accidentally left open and called on our behalf.

4. Also at about 16, a group of my friends and I were horsing around at Graceland shopping center, jumping up and smacking a high awning. We were mainly just seeing who could jump higher and not trying to vandalize it. A patrol car slowed down and warned us to knock it off.

5. At 17, I took a late-night walk, and ended up near some closed office buildings. A patrol car came to make sure I wasn't vandalizing the buildings or trying to break in. I was in sort of a bleak mood that night, prompting them to give me the "Problems at home?" quiz. I passed, apparently, and they shood me on, asking me only to stay on the sidewalk so as not to look like a prowler.

6. At 18, my car was in the shop, and I wanted a late-night snack, so I walked down to a local gas station. I took a shortcut back home, crossing through a car dealership and onto the train tracks behind it (Jack Maxton Chevrolet by 161 and Proprietors, if you're familiar with Worthington). Unbeknownst to me, a car had recently been stolen there the previous night, so the police were patrolling around it more. An officer jogged up to me on the railroad tracks, but saw that I was just drinking my Mountain Dew and strolling along, so he explained all this to me. When he asked my name, he even went so far as to say I wasn't obligated to answer. I cooperated, said I'd stick to the sidewalks in the future, and he let me go.

7. My first speeding ticket, and the first time I thought I was about to get shot. At 18, I thought I was invincible behind the wheel of a car, and took late-night drives through the hilly backroads between Worthington and Linworth, and just went nuts, flying around curves, pedal pegged. During one of these outings, a cop passed me going the other way. For some reason, I assumed he wouldn't even try to turn around and catch up to me. About a mile and a half later, I was proven wrong when I saw his lights in my rear-view mirror.

I pulled over, and I knew that I would be asked for my registration, which was in the glove box... you can see where this is going, can't you? As the officer approached my window, he saw me rooting around in the glove box, and barked out a sharp "HANDS ON THE WHEEL!". I complied immediately. He followed this by questions about my drinking (none, by the way, I didn't start drinking until my late 30s), how he'd like nothing more than to haul me away to jail, but a moving violation wasn't enough cause, and he left me with a ticket, and went on his way.

A lot of that was basic "scared straight" material, which I saw for what it was, but I reflected a lot on how he seemed ready to draw on me when he saw me in the glove box, and I decided to stop driving like a maniac. In hindsight, this probably saved my life, as I was less likely to wreck in an infrequently traveled backroad in the middle of the night.

8. At 19, my cousin Glenn and I were driving back from a city east of Winston Salem, NC (possibly Raleigh, but I can't remember for sure) where we were helping to open a new "Shoe Show" store. I was a passenger, and Glenn was trying to make good time on the way back. A state trooper pulled him over for speeding, and asked him to step out of the car.

As it turns out, this wasn't a bad thing, the officer just wanted to scold Glenn in private rather than embarrass him in front of me (southern politeness - I was still sort of a kid, making Glenn, about 10 years my senior, an authority figure by default. It would demean that authority to get publicly scolded. This probably sounds confusing to you Yankees, but that type of thing is a standard tenet of our culture). Glenn was completely "yes, sir" and "no, sir" to the officer, who let him off with a warning.

9. At 19, I was a passenger in a car with my friend Steve, who suffers from sleep apnea. We were both beat after coming home from either a party or a concert, and he swerved a little, and was pulled over. After the officer assessed that we were both just tired and not drunk, he told Steve to be careful and try to get off the road soon and find a bed.

10. At 20, I would typically close the pizza store I worked at, and then head off to a 24 hour gym to work out before I went home. On one particular night, I went flying through a speed trap, and was pulled over. The officer asked me where I was going in such a hurry. "World's Gym," I replied.

As luck would have it, that was the gym that a lot of police officers worked out at. I was let go with a warning (possibly from the serendipitousness of my destination), and also informed that one of my brake lights was out.

11. At the tail-end of my reckless youth, I liked to play on playgrounds in the middle of the night with friends. On one particular night, my friend Lisa and I stopped by Colonial Hills Elementary at about midnight after picking up some Jolly Pirate donuts. We sat on top of the school's jungle gym, ate our donuts, and chatted.

After a while, a cruiser pulled up and shone its lights at us. The officer asked what we were doing, and I flashed him the Jolly Pirate bag I was holding. "Just eating some donuts". He then asked our ages (18 for her, 20 for me), and then told us simply to "stay out of trouble". He left, without even demanding we leave the school.

12. At 21, the pizza store I worked for had run out of an ingredient, and I was sent to another store to borrow some. Trying to hurry back, I ended up read-ending someone who stopped suddenly. The police arrived to take a report, where I admitted I was at fault and was cited for unassured clear distance.

13. Also at about 21, I was pulled over for speeding on the West Virginia turnpike. The state trooper invited me back to his patrol car, where I sat in the front as he filled out my ticket. He was very chatty, and was listening to classic rock in his car. I think maybe he was just lonely and wanted someone to talk to. Nice guy, if you don't count that he gave me a $60 ticket.

14. At 22, I was an assistant manager at a pizza store, and had a free night with nothing to do at 12:30am. I decided to play a prank on that night's closing manager, so I parked in the empty lot next to our store and snuck over, then quickly unlocked the back door and jumped in to the suprise of the people doing closing cleaning and paperwork.

Meanwhile, a patrol noticed my car in an empty parking lot, and ran my plates. By some means, they put two and two together and phoned the store and asked if I was inside... then asked me to come outside. I did, and the two officers spread out around me until they formed an equilateral triangle with me as the third point. They were clearly on edge and expecting trouble.

It turned out that I had never paid my ticket from number 13. Combine that with my car being in a vacant parking lot, and they thought maybe I was a criminal robbing the store. A few minutes of conversation assured them otherwise, and they ended up not citing me with anything, but taking my car's license plates (!) until the matter with the West Virginia tickets was resolved.

I'm not sure if taking my plates was legal or warranted, and it did come close to causing me to lose my job (managers have to be able to drive). I managed to get the ticket cleared up in a few days, and got my plates returned to me, so there wasn't any long-term consequence.

15. Also as 22, shortly before stepping down from pizza management to the less stressful and equal paying job of delivery boy, an officer came into my store to pick up a pizza. This happened a lot, and I haven't listed the score or so times I've handed an officer a pie and told him to have a nice day. In this instance, however, a young man, college age, who was in the store prior to the officer's arrival stiffened and was visibly nervous. His order came up first, so I handed it to him. He said an abrupt "thanks", and quickly left the store.

After he left, I mentally played back the conversation he had with Dave, my inside closing help that night, and didn't remember him ringing the man up. "Did he pay?" I called to Dave. He replied "I thought you rung him up."

Without speaking to us, the officer (Shicks, I think, from the Westerville police) got on his shirt-mounted CB and called for a car to come pull the guy over as he drove away. Being a trained observer, he knew the make, model, and color of the car, the road the car left on and which direction he went.

About 10 seconds later a police car with lights flashing came flying past the store. About 5 minutes after that, the ghost-white, shaking man came back in, stammered out "I'm so sorry," and paid for his food. Our running theory is that he was holding, and thought he was about to get busted. To my knowledge, the officers didn't pursue that angle. Scaring the crap out of a college boy is more fun than a nickle-bag bust, I imagine, plus the amount of paperwork to show probable cause for a search was probably insane back in the pre-9/11 days.

16. At 23, an SUV rear-ended my Ford Escort, smashing my back window and cleaning my clock pretty badly. An officer ticketed the man who hit me, made sure I was ok and didn't need a doctor, and called a tow-truck for me.

17. Also at 23, I was booking back to the pizza store at 1:45am after making my final delivery one Saturday night, and went a little left of center on the final left-turn onto the road the store was on. An officer pulled me over, and sat there until backup arrived. Then both officers exited their cars, one approached my driver's-side window, the other took a vantage point behind my car and to the right.

So basically I'm sitting there with my store driver's hat on, the empty pizza bags beside me, and about a block from the store. Despite that, I was at first unable to convince the officers that I was working and on my way to the store, rather than going home from a bar or a party. "How much have you had to drink tonight?" came up more than once. I blew a 0.0 on their portable breathalyzer, naturally, and they then accepted my story, and let me go without a ticket. Possibly that was their way of apologizing for the wrong assumption.

18. Again at 23, near the time I stopped working pizza, I was asked to give one of the teenage counter-girls a ride home since her ride fell through. I combined this with a delivery going the other direction, so I sped a little so I could finish the delivery, drop her off, and get back to the store quicker, as we were short-staffed on drivers that night. I was pulled over for speeding, however, making my efforts at timesaving moot.

It was near Christmas, and the young lady riding with me, fit and lovely, was wearing a snug sweater that the officer was visibly distracted by. He casually and quickly gave the standard warning speach "Hey, it's close to the holidays, and kids are out going wild, be careful on the streets... man, that's a nice sweater!" I was let off with a warning, which I attribute to Tracy's charm and the young officer's libido.

19. At 24, I had quit pizza, started working at CompuServe, and moved my girlfriend in with me. She would later become my wife, and later still would become my ex-wife. I received a phone call one evening when she and I were watching television. The call was from a police officer who introduced himself politely, asked if I was Gayle's son, and said that she and her friend needed a lift home.

I got the address, and my girlfriend and I went to pick them up. On arrival, the officer gave me the full story. He pulled them over for drunk driving, and was more interested to see that they got home safely than to cite anyone (my mom and her friends were pretty entertaining and likeable back in her party days, which probably helped). I said thanks, my girlfriend and I each drove a car, and no one got ticketed or sent to the drunk tank.

20. At 25, I let my tags expire. Life with a new baby was sort of hectic, which I rationalized as an excuse to keep procrastinating. I stopped by the bank on my morning commute one day, and wanted to finish my business and get to work as soon as possible. The side road the bank was on intersected a major road (Sawmill) and a block down the main road to the left was a stoplight. The light had just changed to green, sending traffic my way, and I had the opportunity to beat the traffic, provided I blew a stop sign. I scanned for pedestrians or other obstructions, and punched it, pulling in just ahead of the first car.

I pulled into the left turn lane (for Snouffer), and got caught at the light. Mozying up behind me came the first car from the previous light, a Columbus police officer. And he sat there and waited. And I spent the next 90 seconds thinking about all the opportunities I had to renew my tags but decided not to. The light changed, his lights came on, and I took my lumps (figuratively). I think the ticket for the stop sign and driving on expired tags was a little north of $100.

21. At 27, my wife and I took a vacation to North Carolina with our toddler daughter, and decided to stop at a hotel in West Virginia when little Stacey started getting fussy. While driving down a service road to the hotel, a police car coming the other way stopped and turned his emergency lights on and approached us on foot, cautiously.

"Where you guys heading?" asked the officer "Yon hotel," I said, pointing. I probably didn't say "yon hotel".

He looked us up and down, shone his flashlight inside our car, and explained that we were driving the same make and model of a car they were looking for. He didn't say what the guy in the car was wanted for, but after assuring himself that no one was hiding in our floorboards, he tipped his hat, bid us good day, and ambled back to his car. He probably didn't bid us good day.

22. At 30, my first wife and I had split up, and I was for a few months dating a woman in Kirkersville when I was living in Dublin. A few times a week, I would trek the 40 miles to her house, play with her kids, go out to dinner, and trek back home. She was great, her kids were great, and despite our good relationship, we just sort of stopped calling each other. My assumption has always been that Tia looked up my court records and saw that my divorce wasn't actually finalized like I told her it was. I felt like an asshole for a long time after we stopped seeing each other, especially for how her 8 year old would feel abandoned by me. Thinking about little Merica being sad was the main reason I didn't date anyone else for the following 7 years.

Anyway, police, right... During that time, I drove this little Saturn whose previous owner drove the hell out of it. Shortly after I bought the car, a host of things started to go wrong with it faster than I could afford to get them repaired. During one of my 40 mile treks back from Kirkersville, my headlights went out. My parking lights still worked, and so did my brights. It was about 11pm on a weekday when I was heading back, so there wasn't much traffic. I alternated between driving with my brights on, and switching to just parking lights when a car came from the opposite direction, so as not to blind them.

I made it almost all the way home, and then about half a mile from the freeway exit back to my neighborhood, a cop pulled me over to see what was going on. I explained the situation, and promised to get the car to a shop come daylight. He advised me just to leave my brights on and not worry about blinding people, and let me go.

23. At 32, I was at the apex of a horrible undiagnosed sinus infection that would probably eventually have killed me had I not found a good ENT to perform a septoplatsy. For about 6 months, I kept going to my family doctor complaining of headaches that put pressure on my eyes and teeth, but for whatever reason the idea that I might have a sinus problem never crossed his mind. He would load me up on vicodin under the assumption that I had cluster headaches. After finding that they didn't fully alleviate the pain, but wanted to take them anyway, I threw them away to avoid becoming an addict, and switched to ibuprofen and benadryl, which combined to make life tolerable.

During the next famliy get-together in North Carolina, I had an attack, and on the way back took a dose of my mother's benadryl, which was, in hindsight, a much stronger dose than my body was used to taking. I was driving her and 7 year old Stacey back to Ohio, and progressively getting more drowsy.

After passing Wytheville, Virginia, we came to the Big Walker Mountain Tunnel, a quiet, dark oasis from the noisy, bright freeway. After passing through it's 4/5ths of a mile, I was lulled nearly to sleep, and my foot kept getting heavier on the accelerator. I exited the tunnel going about 70 (55 is the speed limit from about 1/4 mile before to 1/4 mile after the tunnel), to the waiting speed trap on the other side.

Seeing my speedometer be nowhere near where I thought it was, combined with the flashing lights, I got a jolt of adrenalin, counteracting the diphenhydramine-induced coma I was heading towards. I uneventfully signed for my ticket, drove the remainder of the trip fully awake, and wrote my speeding users-fee check a few days later.

24. At 37, I fell victim to a stop sign trap at the corner of College ave. and Nicole in Westerville. When I first moved to Westerville, the stop sign was one street to the west, at the corner of College ave. and College ct., where it was immediately adjacent to the Middle School. A local petition was circulated for a ballot initiative to move the stop sign to Nicole, which has more houses on it. With the sign moved, the kids can immediately cross College from Nicole, then walk a block to their school, instead of walking down College for a block, then crossing immediately to their school. This is another reason why the rest of the world shakes their head at us and the obsession we have with our first-world problems.

Anyway, I drive past that stop-sign on the way to the freeway in the morning about an hour after the Middle School classes start, and until then I had just slowed down and looked for oncoming cars or kids late for school, and coasted through the stop sign at a slow crawl. Westerville posted a crusier down Nicole far enough to not be recognized as a threat by folks like myself who coasted through the stop sign, and I'm assuming pulled over about 20 people that day, netting the city an easy $2 grand.

After being pulled over, the officer asked me "Do you know why I pulled you over?". "Yes," I replied, and then bit my tongue to avoid blurting out any smartass comments about it being the end of the month and time for local police to "pay the rent", or my being more concerned with where pedestrians were than hidden patrol cars.

My ticket was over $100, due a week later. I hate the suburbs.

25. At 38, a friend and I drove up to Cleveland to see a band whose bassist we went to High School with. On the way back, my friend had to pee, so we pulled over on the freeway and he started to head to the bushes. A state trooper pulled over then, and asked us if everything was alright. "I'm sorry, officer, I just really need to pee," says my friend. The officer replies "alright, then, just making sure your car wasn't broken down."

I'm pretty sure it's a violation of some sort to stop on the freeway to pee in the bushes, but the trooper was less concerned about that than the possibility that someone might need help.

26. At 40, again with the expired tags. This time I was just heading to the grocery store with my pregnant wife, and driving "safely" - in my opinion, I always drive safely; this time I just wasn't breaking any traffic laws. The officer who pulled me over let me off with a warning in return for a promise to renew the tags soon.

So what can we make of all this? How could I have had all these encounters with cops and not been victimized, arrested, pepper-sprayed, cuffed, been threatened with dogs, or subjected to searches without probable cause? Well, being a white male probably skews things in my favor, I'll admit, but 26 times all ending without incident? Something else is at play.

Maybe the way I behave matters. I give cops respect and cooperation as a rule, and knowing that they quickly divide people into the "might kill me" and "probably won't kill me" categories, I try an awful lot to look like the latter, especially after my wakeup call when I was 18 and not thinking about how rooting around in a glove box might look. They do have jobs that put them in harm's way, obviously, and getting home without injury is going to weigh on them stronger than what I think my constitutional rights are. A pragmatic rule of thumb is cooperate on the street, object in the courtroom. In my case, doing much of the former has meant I needed to do none of the latter. Your mileage may vary.

I think what matters most, though, is that the negative stories you hear about corrupt police, OWS protestors getting smacked around, and adrenaline junkies with badges are mainly the exceptions to the rule. Most of the police are the good guys. If that weren't the case, I think I'd definitely have a different story to tell.

Think of the children!!

2011-11-23T14:51:00.001-05:00

No seriously, think of the children. And not the bounty.

About a month ago, I listened to an NPR story on "All Things Considered" on my drive home from work, which concerned Native American children in South Dakota being declared "neglected" in high numbers, and being removed from their families and put up for adoption. The implication is that the South Dakota government was using a financial incentive as an excuse to go all Captain Pratt on the natives, killing the Indian and saving the man, by means of placing their kids in white homes. The text version of the NPR story is available here.

Some background on the NPR story:

In 1997, HR 867 was enacted by Bill Clinton, ammending section 473 of Part E (Federal Payments for Foster Care and Adoption Assistance) of title IV of the Social Security Act with some seemingly good-intentioned language, which had some disturbing consequences. Section 473a now contains this (ellipses, brackets, and sentence reformatting are mine):

...the adoption incentive payment payable to a State ... shall be equal to the sum of $4,000, multiplied by the amount (if any) by which the number of foster child adoptions in the State during the fiscal year exceeds the base number of [same]; and $2,000, multiplied by the amount (if any) by which the number of special needs adoptions in the State during the fiscal year exceeds the base number of [same]

In 2008, the 110th Congress passed Public Law 110–351 (the "Fostering Connections to Success and Increasing Adoptions Act") which upped this last amount to $4,000, making the total take for getting a special needs kid adopted $8,000.

In basic English, one would assume "special needs" refers to children with mental retardation, epilepsy, behavioral problems, or other conditions requiring specialized care - basically kids that don't fit the happy suburban white couple Disney mold of the perfect kid to adopt. Title IV-E disagrees with that assumption, though. It's context of "special needs" implies only things that would make it harder to place a child with an adoptive family without a financial incentive. It states in section 473c:

the child shall not be considered a child with special needs unless ... the State had first determined (A) that there exists with respect to the child a specific factor or condition (such as his ethnic background...)

This language basically invites states to declare all their black or native populations as special needs. A quick glance at the Child Welfare Information Gateway's Adoption Assistance by State page shows that many states have done just that. The two I want to focus on have been in the news recently for abuses by their Child Protective Services departments: South Dakota in regard to natives, and Virginia in regard to something a little more subtle.

South Dakota's categories for special needs:

Eight years of age or older
Race or religion (Native American)
Member of a sibling group to be placed together for adoption
Physical, emotional, neurological, or intellectual handicap or problem
Need of a prosthesis, extensive, on-going, or anticipated medical care, or therapy for speech, physical, or psychological problems
Adoption by foster parents with whom the child is living is the only appropriate permanency plan

And Virginia's:

Six years of age or older
Member of a minority race
Member of a sibling group that is ready for placement at the same time and should not be separated
A physical, mental, or emotional disability
Hereditary tendency, congenital problem or birth injury resulting in a substantial risk of future disability
A child with a physical, mental, emotional disability or hereditary tendency, congenital problem or birth injury present at the time of adoption but not diagnosed until up to one year after the final order is entered

Does "birth injury" sound a little vague? Hold that thought.

Combine the $8,000 per head federal assistance with defining an entire race of people as harder to adopt, and you have just created a financial incentive to err on the side of removing minority children from their families.

The NPR story focussed on one particular group of kids who were seized from a family guilty of nothing more than poverty, and who had community and extended family childcare available. The story ends on sort of an up-note: A tribal council passed a resolution warning the state of South Dakota that criminal kidnapping charges would be filed if the kids weren't returned. They were returned, along with some snarky comments in the vein of "we can still come take your kids with impunity, so watch your step, Tonto." (The "Tonto" was silent, but implied.) The family of the kids is very worried by those comments, but to me they were an admission of defeat, the bully's retreating "I'll kick your ass" after getting knocked down by his intended victim.

For what it's worth, South Dakota responded to the NPR story, basically declaring their innocence and good intentions, falling just shy of espousing the "white man's burden".

I thought that was the end of it, some Black Hills comeuppance by natives who have been systematically harassed and disenfranchised by whites for centuries, and finally landed a good blow to them. But it isn't. A seemingly unrelated scandal is going on currently in Virginia, and was publicly called out in the Washington Examiner.

In Baby Sabrina's case, there was enough going on to make it a case worth a quick peek by Virginia CPS, namely a diagnosis of "failure to thrive". My reading of the issue on the mom's website is that Nancy was having trouble breastfeeding. The baby lost weight after birth, which all kids do, but did not then regain the lost weight, and in fact over the next weeks lost an additional couple of ounces. Sabrina was admitted to the hospital, fed a lot of formula, and then started gaining weight.

CPS investigated, which they were well within their right to do. Losing weight immediately after birth is par for the course, but a healthy baby who isn't being neglected should recover soon. Sabrina didn't. When CPS investigated, the correct response should have been "thanks for being concerned about our baby. We're trying hard, and now the doctors are helping, and we'll comply with their recommendations because we want nothing more than for Sabrina to be healthy." What they said instead was "fuck you, we're getting a lawyer," which raised the ire of the CPS.

From there, I would have expected a quick resolution, possibly with CPS backing off, or possibly with them temporarily placing the baby with Nancy's mom. Instead, they removed the baby from the family, and put it up for adoption. Why? Two reasons. First, because you don't stand up to the man; he's a spiteful son of a bitch. Second, the "failure to thrive" diagnosis fits well with the Virginia special needs category of "birth injury resulting in a substantial risk of future disability".

In my opinion, and I have nothing to back this up other than a gut feeling, Sabrina's possible status as special needs caused Virginia CPS to side with removal and adoption outside the family, rather than just monitoring or placing her with grandma. Even though the state's legal costs quickly surpassed the $8,000 take. Nancy's site does have a good deal of atrocity propaganda on it, and it's hard to read through that and find the true story, but there are enough questions about the case that it should at least be heard by a federal judge. Maybe they're full of crap and were truly neglectful, or maybe Virginia CPS overstepped, but either way they should get their day in court.

Maybe neither the South Dakota nor Virginia cases are caused by official state evil. Maybe the intentions are always good, with an eye on protecting children and giving them the best homes possible, and after seeing enough bad in the truly neglectful parents, CPS case workers see bad in all parents. I don't know, but I do know that there is a conflict of interest for any state that accepts per-child adoption bounties. Yes, a little rhetorical, but a bounty is what it is. The spirit of the law is to use the money when standard attempts to place the child have failed, but in Sabrina's case as with the South Dakota case, an acceptable placement was available and ignored. So there is at least the perception, a revealed preference, that underfunded state CPS agencies now have an eye on potential federal money, and skew their cases accordingly.

No matter the true nature of the South Dakota and Virginia cases, adding this motivation for funding into organizations tasked with removing children from their homes is a powderkeg, especially in today's world of protesters fighting the police, unemployment bringing children into poverty, and the simple fact that parents who feel their children are threatened are irrational, more likely to put up their dukes than to investigate the proper appeals process. The 473a ammendment to Title IV-E will be responsible for needlessly breaking up families, and for police, social workers, parents, or children getting injured or worse. And it needs to be repealed.

Tinkering with Calculus

2011-10-30T16:17:00.001-04:00

A little document I whipped up on Google Docs after dusting off a calculus book:

Adelaide

2011-10-16T13:08:00.001-04:00

Adelaide Lenora Allerding
October 14, 2011 4:20am
6lbs 12oz, 19.5"

As I mentioned a while back, my wife and I decided to have a baby. It's an easy time for us to have a baby, because I have a stable job, I'm still young enough and healthy enough, our marriage is strong, Liberty and I agree on most things, and Liberty has a strong support network of family and friends. It's a hard time for us to have a baby because I am no longer happy working corporate IT, or living in Ohio, Liberty is unemployed and has a mountain of student loan debt, the house is falling apart, and although I'm healthy now at 40, I'm worried about what my health will be in 10 years at 50. The more I dwell on these negatives, in fact, the grayer my hair seems to get.

In our shared opinion, the easy outweighed the hard, but if we didn't think that was so, we probably would have had a baby anyway. Because we both love babies, and each other, and, you know... come at me, bro. Just bring it, world. Rain some more bad on us and see who's still standing tomorrow.

Liberty was originally due on October 12, according to the pregnancy wheel used by our CHOICE midwife, Audra. We planned to drive down to "The Farm" in Tennessee, home to Ina May Gaskin, and rent one of their birthing cabins for a month and have the baby there. (Even though we are the 99%, as the protest saying goes, and it would have taken more cash than I could comfortably afford, with no guarantee that insurance would cover any of it -- see "come at me, bro" above.) We would see local midwives here at the CHOICE center, and when she seemed close to ready for labor, we would truck on down south to spend a month on The Farm. That was the plan, anyway.

Throughout the pregnancy, Liberty had stomach pains that were pretty severe. She was diagnosed as having H. Pylori, easily treated with some hard core antibiotics whose side effects include birth defects and miscarriages. So instead she suffered the entire pregnancy, nursing her way through the pain with probiotics, red raspberry/nettle tea, and other herbal stomach aids.

Whether a direct result of the stomach problem or coincidental to it, the baby was the wrong size late in the second trimester. The midwives weren't sure if the due date was correct, if a lull in growth was baseline for how Liberty made babies, or if there was a nutrition or development problem. So we did what we had been trying explicitly to avoid: started medicalizing the pregnancy. We got a few ultrasounds over the next month, Liberty started making appointments at the Department of Health for various tests and labwork, and The Farm dropped us as clients.

The last was a bad blow, and Liberty was inconsolable for a few days. "I tried to do everything right," she said during the worst of it. A guy needs to fix things, it's just how we're made, and I could do nothing to either attack the problem or comfort my wife. I still get a little choked up when I think about it.

CHOICE kept us as clients, and the baby made up for lost time over the next few weeks, due either to providence's original plan, or Liberty forcing down food she knew was going to make her feel like hell in a couple hours. As the original due date approached, the baby was the right size, no problems were indicated on ultrasound or blood tests, and we planned for a home birth. Audra and another midwife, Amy, came for a home visit, gave us a kit of baby making stuff including pads to catch blood and stuff, instructions I was to memorize in case we couldn't get help in time ("if the umbilical cord seems looped around the neck..." I was really hoping it wouldn't come down to me being Liberty's only help in delivery), and the ominous infant resuscitation board. Just in case.

Just imagine living with your pregnant wife for a couple months with an infant resuscitation board in your bedroom. Just think about that for a minute.

On Thursday, October 13 at about 10pm, Liberty's behavior changed, and her contractions were visibly making her more uncomfortable than usual. (For those not in the know, pregnant women have contractions pretty much all the time in the third trimester. Not constantly, but most days there will be at least a few, growing in regularity and duration. When this happens, the stomach gets rock hard. It's pretty wild.) Anyway, I figured this was it, so I went down and made some coffee, got re-dressed, and started pitching the idea of calling Audra.

At 11, Liberty made the first call. With a midwife now on standby, Liberty tried to take a warm bath to see if the contractions would pass. I drank my coffee, and went in to check on Scout. She was awake, as we were making plenty of noise. "I think your mom's in labor," I said to her, "this can take a long time, so try to get some rest, and I'll come wake you up if anything interesting happens." Naturally she didn't sleep any more, nor, I'm pretty sure, did she try to.

The bath didn't help. Liberty's pain level got worse, and the contractions got stronger. I made the second call to Audra at about 12:15, as Liberty was reduced to communicating through head nods and shakes. "I think we need you," I said, and hearing Liberty's cries in the background, she said she would get ready and come over. She showed up about a half hour later, and Amy shortly after that.

At about 1:30, I could hear Scout rustling around, and I checked on her again. She wanted to come help. Liberty and the midwives were all OK with her coming in, so she did. Throughout the labor, little Scout was ..and again, I'm choking up just thinking about it... the absolute best that humanity has to offer. She watched quietly, whispered a few questions to Amy, held mom's hand and patted her hair, ran to get water or juice when mom was thirsty, and held it to her mouth so she could drink from the straw if she didn't have a free hand to hold her own cup. I told her later how proud I was of her, and I swear I felt as much love for her then as I did when little Stacey explained to me how the sunset was medicine for the sky.

It was a little scary for Scout, watching her mom in pain, and I geared up to give her the following consoling speech: "Angel, do you see how the midwives faces are all calm and relaxed? They've seen a lot of deliveries before, and they know this is all normal. See how they don't looked worried?" Before I started to say that, though, I looked at their faces. I saw something hiding behind the relaxed expressions. Concern. Worry. The feeling that something isn't right. The problem was that everything seemed to be going normally, but Liberty was in much more pain than she should be. So I withheld my reassuring speech, and waited for the problem to reveal itself.

It did so very soon thereafter. Liberty became completely dilated and effaced, and as soon as she started pushing, the baby's heartbeat dropped to about 80, by my estimate. A midwife pitched her voice low and said softly to the other "that's too low." They gave Liberty oxygen, told her to lie on her left side (I think it was the left side), and try not to push for a minute. The baby's heart rate came back up, but not quite to where it should have been. The next push, the problem was still there. "We might need to go to the hospital," a midwife said.

I put on my socks and shoes, got some socks for Scout and told her to go put them on with her boots, and I ran down to get her a coat. By then, the plan was definite: we would leave for the hospital immediately. Liberty and Amy would ride in the back of my car, Audra would call the hospital, canvas the house, and follow. I helped Liberty, now in pain, scared, and confused ("what's happening?!" a near sob, "what are we doing?") out of the house to the car. Amy barked an order to remove Scout's car seat, which I did, and directed Liberty to get on her hands an knees in the back, which she did. Amy got in beside Liberty and reaffixed the oxygen mask, I got Scout buckled into her car seat in the front, made sure everyone was ready...

And I put the God-damned hammer down.

It was 4 in the morning, and the streets from my house to St. Ann's were nearly vacant. We pulled up to the hospital about 5 minutes after we left the house, including two blown stop signs, a left turn on red, and a 90 in a 45.

Amy went in to get a wheelchair, and I got Liberty out and started walking her to the door. Scout followed along, and had an almost pleasant look to her. Very calm, inquisitive even. "What's all this crazy driving and running to the hospital all about?" The ladies went in together while I parked the car, and by the time I made it in the hospital everyone was gone. I had a brief conversation with the security guard:

"Hey, there was a pregnant woman in a wheelchair..."

While pointing to the elevator, "Second floor."

I got off on the second floor, which on first glance was a ghost town. The receptionist's desk was empty, and the security doors allowing one back to the delivery rooms were closing. I dashed to them and grabbed one before it closed, and slipped into the secure area. I heard the sounds of people around a corner to my right, and headed over that way purposefully, damned near storming up to the nurse's station. "LIBERTY ALLERDING!" If you know me at all, you know that this is completely out of character for me. Yelling at people at a nurse's station is as unlikely a thing to happen as me pushing people out of the way at Disney World... which I also did when I realized 6 year old Stacey wasn't beside me any more. Issues with my kids tend to bring to the surface that testosterone response I'm always suppressing.

Anyway, before I leapt the desk and started rifling through charts, a very nice and polite lady told me where she was, and asked me first to come to the reception area to give them my insurance card, date of birth, and whatnot. She took the information quickly, and I went to the delivery room and caught the last bit of the action: My wife in exactly the position she had been trying to avoid for the entire pregnancy: surrounded by doctors, on a delivery table, legs in stirrups.

Strangely, the delivery at this point was completely uneventful. "Push!", "OK, I have the head, one more!", "Waah!". Adelaide was delivered naturally, all things considered, at 4:20am, a fact that will give all the heads she meets no end of giggles.

The St. Ann's staff was everything I thought they wouldn't be. They were polite, they took our direction (no episiotomy, leave the baby with us instead of taking it to the nursery), they waited for Adelaide to pink up before clamping the umbilical cord, and only offered token resistance when Liberty said not to stitch her tears up. Despite being lit up with testosterone and unable to keep my legs from shaking as I watched, I only said one cross thing to the staff: "She said no, leave it at that."

A side note here: This isn't my story, and while I'm writing it from my point of view, I don't intend for this to look like it was all about me. This is Liberty's story, slowly pushed off the course she had for a pregnancy and labor experience, but nonetheless emerging victorious. She did all the suffering, and my actions, despite their comedic value and reflection of how much I care for Liberty, could have been performed by a chauffeur just as easily. And a personal assistant. And a bodyguard. But still, her story. I'm not the hero, I can just only report what I saw.

We asked to be released from the hospital as soon as we could, which we thought at first was going to involve staying at least 24 hours for observation since the labor was problematic. At this point we realized that Liberty and Scout were wearing nightgowns, and Liberty didn't have her purse or shoes, and no one had a toothbrush. And little Adelaide had no clothes and her car seat was disassembled at the house, since we didn't expect to need it for a while. So I drove home, obeying many more traffic laws than the trip to the hospital, packed up a bag of stuff, put the car seat together, and came back to find that we were being released.

Adelaide's responses were all normal (I think someone said "8, 9, and 9", referring to some reflex/awareness test), the delivery was vaginal with no cutting, and mom was coherent, so there was no reason to keep us. Another plus for St. Ann's in my book: "You seem OK, take off and let us know if you need anything." So, good on them for being more supportive of moms and less interventionist. And good on the ladies at CHOICE who were humble enough to see when more help was needed, but strong enough to continue to advocate for Liberty at the hospital.

Naturally I'm proud of Liberty for enduring both monumental suffering and indignity, and little Adelaide for hanging in there and coming out healthy. But when I think back over the whole affair, my strongest memory is of Scout and a cup of juice held out to her mom, the fearlessness when things started to go wrong, and the excitement at getting to meet her sister.

Designing a Notes iPhone web app

2011-04-22T11:48:00.000-04:00

"A pedagogical decision hides behind every design decision" -Dan Meyer

For the last few weekends, I've been coding in the early mornings while my wife sleeps beside me, working on a replacement for the broken built-in Notes app on her iPhone. My replacement is usable and stable at this point, and I'm just putting the final polish on the code to remove duplication, improve comments, delete orphan code, etc.

The tools I used to design this are the same as the diet tracker app I wrote for her to track her protein and calcium during her pregnancy: handwritten JavaScript, and Google's appspot.com webserver to properly serve the cache manifest's content type. This was initially going to be a quick hack to learn the API for Web SQL Databases, so I could retrofit database support in the diet tracker, but along the way I learned a lot about designing an HTML Notes application, which was more involved than I anticipated.

This post recounts some of the lessons I learned, and the decisions I made between competing solutions that each had pluses and minuses. Some screenshots of the current product are available below the fold.

Custom icon on iPhone home screen.

Editing: The "back" button on the menu bar is three rectangles and a circle drawn using the HTML5 canvas spec. More on that below.

List: Normally all those minus signs won't be there. The red minus sign at the very top is twisted to indicate being in delete mode. Then each note gets its own minus sign, and twisting them unlocks a delete button. Again, more on that below.

Impetus

The story starts a few years ago when the first iPhone came out. I bought one for Liberty, and it quickly became the source of many pictures of Scout, and of our adventures - pictures that we didn't want to lose. Because of the fear of losing these images, we rarely synced the phone with iTunes, always backing the images up first, and fearing the bad things that would happen when newer iOS versions were installed.

During syncing, we've lost music, saw the built-in applications get slower, had mysterious timeouts backing up data, but fortunately have never lost any of the images. Since each upgrade seemed to make the whole system slower, and assuming newer OS versions would need even more horsepower, syncing again would make the phone virtually unusable.

"Why not upgrade to an iPhone 4" you ask? I've pitched this idea to Liberty, which she soundly dismissed. Her reason: the newer iPhones look more boxy, whereas the original looks curvy and sleek. Well, there's no arguing with that logic... or at least, I don't really know where I'd start, so there's nothing for it but to help her use the phone she has.

The current state of her phone is iOS 3.1.3 with the version of Safari using WebKit engine 528.18. Theses specific versions have some anomalies, namely the Notes app tends to break during the upgrade (file permission problems), and Safari's HTML5 support had some minor issues that have since been ironed out (such as placeholders on textarea fields, which I'll get into later).

The Notes app breaking was the real impetus of this project. Our symptoms consist of the app opening fine, but clicking on most of the notes results in the app simply closing. Only one note opens, but trying to alter it also results in the app closing. There are some suggestions for fixes online, which mainly involve monkeying around with the Settings app and trying again, but those haven't worked for us.

Unix hacker that I am, I could jailbreak the phone, install an SSH daemon, then connect from my PC and do some commandline chmods on the note files, but Liberty didn't like the idea of me hacking her phone like that. One of the things that is helping the two of us have a successful marriage is my not fixating on things like this like I would have a decade ago. If she wants an older phone with an unaltered OS, then that's the environment I work in. If the puzzle is hard to solve under those conditions, so much the better: the puzzle is the fun part. Solving the puzzle is the main focus, not advocacy for being modern or edgy (whatever that means).

When I finished the diet tracker app enough to be usable, I looked for another app to write to learn web databases, and the broken Notes app was the obvious candidate. And so, I began.

My previous blog entry on the diet tracker web app shows (along with my radical views on childbirth) some basics of using offline application caches, and how to turn a website bookmarked to the iPhone home screen into something that behaves like a native application, so I won't dwell on those points here. Let's start instead with databases.

Web Databases

There are two basic flavors of JavaScript accessible local databases: the Web SQL Database, which is supported in WebKit browsers (Chrome and Safari), and the Indexed Database API. The latter was proposed by Oracle a couple years ago, and currently the W3C is declaring Web SQL a deprecated standard. The newer standard has been adopted by Firefox 4, so Wikipedia tells me, as well as Chrome 11 (meaning support for it should be rolled back into WebKit in the near future, propagating to Safari and Chromium). For now, though, Web SQL is what's available to me for iPhone web apps, and that is what I used.

In Web SQL, the method window.openDatabase() returns a handle to a database object. You pass that method a few variables - the local and friendly names of the database, its version number, and the number of bytes that should be allocated for it - and the browser uses a built-in instance of SQLite to attempt to find or create the database.

A SQL transaction function, (transaction handle).executeSql(), can be created that specifies the SQL to execute, any variables to substitute for question marks in the SQL, and asynchronous functions to call on the success or failure of the SQL statement.

The database handle and the transaction function are married together with an odd construct, resulting in code that can look like this:


var db = openDatabase('etchnotes', '1.0', 'etchnotes', 200000);
db.transaction(function(t){
  t.executeSql('SELECT rowid, name FROM notes', [], function(tx, result) {
    var firstName = result.rows.item(0).name;
    // ...do other stuff with results;
  });
});

First, that's too much abstraction and punctuation for my taste; without a lot of familiarity with constructs like the above, it's hard to parse, and harder still find syntax errors in it. But such is the world of asynchronous callbacks.

A slightly better construct is this:


var db = openDatabase('etchnotes', '1.0', 'etchnotes', 200000);
function onSuccess(tx, result) { ...stuff... }
function onFailure(tx, result) { ...stuff... }

db.transaction(function(t){
  t.executeSql('SELECT rowid, name FROM notes', [], onSuccess, onFailure);
});

That reads a lot more clean to me, but I still don't like that the db object can't take SQL directly. To address that, I created a closure function that has a runSql method, opens and initializes the database, and manages its own transactions and error callbacks. This is a simplified version of the closure:


function getNotesDB() {
  var db = openDatabase('etchnotes', '1.0', 'etchnotes', 200000);
  var errorHandler = function(tx, e) { alert("Database error\n" + e.message); }

  this.runSql = function(sql, callback) {
    db.transaction(function(t){
      t.executeSql(sql, [], callback, errorHandler);
    });
  }

  return this;
}

And calling it is a breeze:


var dbClosure = getNotesDB();
dbClosure.runSql("select rowid, name from notes", onSuccess);

After a little exposure, I was able to get my head around async database work, and splitting functions into two parts: the click handler that submits a SQL query, and the callback function that parses the results. I won't dwell on that any more here, but the source code is available below.

Rotating an HTML5 canvas

A standard design pattern on the iPhone is unlocking a delete button. Rather than each removable item having a delete button always present, and an "are you sure?" popup to deal with, some iPhone apps have an edit mode that provides each item with a minus sign on the left. Touching that makes it rotate counter-clockwise, and exposes a hidden delete button for that item. Click the delete button, and the app assumes you knew what you were doing and deletes the item with no verification. Or click the minus button again, and it rotate back to where it was, hiding the delete button. Intuitive and neat, typical of Apple's UI design, and hard to find fault with.

Implementing a similar minus button rotation with JavaScript took a little research, but ultimately wasn't very difficult. The two basic methods I chose between were CSS transforms using something like:


minusButton.style['-webkit-transform'] = "rotate(30deg)";

...and HTML5 canvas context rotations, for example


var ctx = canvas.getContext('2d');
ctx.rotate(angle);
ctx.fillRect(x, y, w, h);

I chose the latter, choosing also to not use image files, but instead to draw the button objects on canvases using paths (think GeneralPath from Java2D). Since all I needed was a circle and a line for a minus button, this was pretty trivial. While rotating the canvas was easy after I figured out to use ctx.translate() to move the origin point to the center of the image, animating the rotation was a little more involved.

I may have been better off using a CSS transition, but having already headed down the path of canvases, I stuck with it, ending up with some arcane looking infrastructure around canvases and their states. Behold the Spinner Factory:


function SpinnerFactory(size) {
  var cr = Math.PI*2;        // Circle
  var deg = Math.PI/180;     // One degree
  var scale = size/100;

  function getScaledContext(obj) {
   // Get canvas context
    var ctx = obj.getContext('2d');

    if (!obj.scaled) {
      ctx.scale(scale, scale);
      ctx.translate(50, 50);
      obj.scaled = true;
    }

    ctx.clearRect(-50, -50, 100, 100);
    return ctx;
  }

  function drawMinus(obj) {
    // Get scaled canvas context, and clear previous image
    var ctx = getScaledContext(obj);
  
    // Red circle
    ctx.fillStyle = 'red';
    ctx.beginPath();
    ctx.arc(0, 0, 50, 0, cr, true);
    ctx.fill();
  
    // White minus sign, rotated to obj.angle degrees
    ctx.save();
    ctx.rotate(obj.angle * deg);
    ctx.fillStyle = 'white';
    ctx.fillRect(-29, -6, 58, 12);
    ctx.restore();
  }

  function spinLeft(obj) { spin(obj, -15, -90); }
  function spinRight(obj) { spin(obj, 15, 0); }
  
  function spin(obj, step, goal) {
    // While spinning, disable object's click handler to prevent competing spins
    if (obj.onclick) {
      obj.deferredOnclick = obj.onclick;
      obj.onclick = null;
    }
    if (step == 0) return;
    if ((step < 0 && obj.angle <= goal) || (step > 0 && obj.angle >= goal)) {
      obj.angle = goal;
      if (obj.nextLeft) {
        obj.nextLeft = false;
        if (obj.unlockCbk != null) obj.unlockCbk();
        obj.unlockObj.style.display = 'block';
      } else {
        obj.nextLeft = true;
        if (obj.lockCbk != null) obj.lockCbk();
        obj.unlockObj.style.display = 'none';
      }
      if (obj.deferredOnclick) {
        obj.onclick = obj.deferredOnclick;
        obj.deferredOnclick = null;
      }
      return;
    }
    obj.angle += step;
    drawMinus(obj);
    setTimeout(function() {spin(obj, step, goal)}, 30);
  }

  this.makeSpinner = function(className, unlockObj, lockCbk) {
    unlockObj.style.display = 'none';
    var cnv = document.createElement('canvas');
    cnv.width = size;
    cnv.height = size;
    cnv.className = className;
    cnv.angle = 0;
    cnv.nextLeft = true;
    cnv.unlockObj = unlockObj;
    cnv.spinRight = function() { spinRight(cnv); }
    cnv.onclick = function(e) {
      cnv.nextLeft ? spinLeft(cnv) : spinRight(cnv);
      e.stopPropagation();
    }
    if (lockCbk != null) cnv.lockCbk = lockCbk;
    drawMinus(cnv);
    return cnv;
  }

}

The Spinner Factory is a JavaScript closure that takes a single variable, size, which determines the diameter of the spinner buttons it creates. Individual spinners are created with the makeSpinner() method, which takes variables for the CSS class name for the spinner, the object to hide/unhide at the end of the spin, and an optional function reference to call after an object is re-locked. Typical usage would look like this:


sf = new SpinnerFactory(30);
item.appendChild(sf.makeSpinner('minusBtn', deleteBtn));

...where "item" is a div tag you want to add a spinner to, and "deleteBtn" is the object that gets unhidden.

After getting all that working, I created some additional methods for the Spinner Factory to use the same scale to draw plus signs and arrows, which don't spin.

Sizing a textarea to fit its content

This was a fun one! After taking great pains to tweak CSS settings to make the note text line up with the lines on the background image, I noticed during testing that if I entered too much text, I couldn't scroll to see it. To complicate matters, mobile Safari doesn't appear to use scrollbars, so there wasn't even an indication that there was more text to see.

After some online searching, I found that you can scroll textareas on the iPhone by using two-fingered swipes. I tested this, and although it worked, it was awkward, and transitions between edit mode (when the keyboard display pops up) and normal viewing mode left the display in unusual positions. I could struggle through it, but it wasn't ideal, and certainly not good enough for my wife.

There are DOM properties for textareas that can be monitored after each character is entered. The one that seemed most important was scrollHeight. It remained constant until any text overflowed off of the screen, then the value changed to the height needed by all the text. This was all independent of font size or the width of the textarea.

I quickly hacked out an event listener that monitored for scrollHeight changes, and set the textarea height to match. Since no scrollbars ever appeared, the user would have no indication that anything interesting was happening. The main problem with this is that the box wouldn't shrink back down if you deleted a bunch of text. The scrollHeight attribute doesn't go below the current height of the textarea. Although not necessarily a showstopper, I didn't like the idea that a user might think there was a lot of whitespace offscreen at the end of the note. I wanted a box that could grow and shrink with the text.

I switched instead to a method that uses a second textarea, hidden offscreen, to make measurements. First, all textareas in this app have some very specific CSS settings for positioning:


textarea {
  border: 0;
  background-image:url('images/paper.png');
  margin:0;
  padding:0;
  padding-left: 13px;
  width: 307px;
  font-size: 17px;
  outline: none;
  font-family: Georgia;
}

Next, some simple CSS tells the "tester" area to hide offscreen (and to turn off scrollbars for testing with desktop Safari).


.tester {
  position: absolute;
  top: -1000px;
  overflow: hidden;
}

And finally the meat:


function textAreaSizer(obj) {
  hiddenTextArea = document.createElement('textarea');
  hiddenTextArea.rows = 20;
  hiddenTextArea.className = 'tester';
  obj.parentElement.appendChild(hiddenTextArea);
  var last = '';

  this.size = function(e) {
    if (last != obj.value) {
      last = obj.value;
      hiddenTextArea.value = obj.value + "\n";
      obj.style.height = hiddenTextArea.scrollHeight + 'px';
    }
  }

  this.size();
}

This closure accepts a textarea as input, and creates a sibling textarea using the "tester" class name. Note that I'm setting the hidden textarea's row size to 20, which means its scrollHeight will never fall below what's needed for 20 rows of text.

The web app in its current state is available here. The source code doesn't try to obfuscate anything, but I still have some commenting and cleanup to do.

Enjoy!

Emulating iPhone rotating buttons with HTML5 canvases

2011-04-13T20:48:00.004-04:00

This is a quick proof of concept tested with Chrome and Safari (which might also work in Firefox... testers?). I'm using timeouts and HTML5 canvas operations to spin buttons, and some DOM tomfoolery to add and remove rows to the document's body. The end result is an approximation of some iPhone settings screens that make you unlock delete buttons before you can remove items.

Enjoy!

HTML5 Web Databases in Chrome, round 1

2011-04-08T08:53:00.000-04:00

New fact of life: To keep up with modern web programming, you need to get your head around asynchronous callbacks. To illustrate, here is a quick script I wrote to experiment with Chrome's JavaScript calls into it's SQLite implementation:

var output = null;

function onSuccess(transaction, result) {
  output = result.rows.item(0).sql;
  console.log('onSuccess completed');
}

function getDB(dbName) {
  var fm = 5*1024*1024; // Five Megs
  var db = openDatabase(dbName, '1.0', dbName, fm);
  console.log('Database opened');

  this.runSql = function(sql) {
    db.readTransaction(function(t){
      t.executeSql(sql, [], onSuccess)
    });
    console.log('runSql completed');
  }

  return this;
}

var joe = getDB('db');
joe.runSql("select * from sqlite_master");
console.log('output: ' + output);
console.log('End of script');

Until it dawned on me that the SQL execution was asynchronous, I spent about 30 minutes chasing my tail trying to find a variable scope problem. In the console debugger, everything seemed to be set right when I manually entered commands one at a time, but the script didn't seem to be setting them when it ran. Didn't seem to be, but it just wasn't happening when I thought.

The above script was a re-write of what I was doing initially, with loggers at each step to show when the "output" variable gets set. Unsurprisingly, it happens on its own good time, not when the "procedural" part of the script reaches the end.

Here's a screenshot of the console output:

The value of "output" is still null when the script reaches its last line. Manually checking the value after onSuccess completes shows that it does get set correctly, just later. So, there you have it. Writing that iPhone app or new web game? Start thinking async.

Rage against the Pitocin-Cesarean Complex

2011-04-06T19:35:00.005-04:00

(and how I wrote my first iPhone web app)

"So I got me a pen and a paper and I made up my own little sign. I said thank you Lord for thinking about me, I'm alive and doing fine." - Five Man Electrical Band

Before rambling about my latest tinkerings, I have a small announcement: My wife and I decided to have a baby. She asked me not to make a big deal about it online, not post a broadcast "guess what?!?!" message on Facebook, and in the spirit of that I won't make flowery pronouncements here about the joys of fatherhood, or starting over at 40, or any of the hundreds of other things I would otherwise go on at length about. But there it is: I'm in love with a woman I think the world of, and at the beginning of January, with our third wedding anniversary near us and neither of us having one foot out the door or buyer's remorse, we decided to stop using birth control and try to have a baby.

By the end of the month, Liberty was pregnant. When she was pregnant with Scout, Liberty wanted as natural and non-medicalized birth as possible, preferably a home birth with a midwife to assist. In Ohio, home birth and birthing centers are in a grey area legally. Instead of outright declaring that birth is only allowed in hospitals, the cost of liability insurance for midwifery prices many centers out of existence, and not all medical insurance plans cover them. Liberty unfortunately could not find a local center who took her insurance, but found one in Cincinnati that did. During a 37th week appointment with them, Liberty's blood pressure was elevated, so her midwife recommended going to a hospital for a urine test. At the hospital, the doctors were quick to diagnose preeclampsia, and demanded that she stay and be induced immediately. Needless to say, this wasn't the birth plan she had in mind.

The hospital tried to enforce the standard medical interventions designed to get the doctor to the golf course by tee time: Pitocin, epidural, Cesarean. Her midwife (bless her heart) went to bat for Liberty, telling them to back the hell off, insisting on a private room with a bathtub, that she be allowed to get up and move around, have access to food to keep her strength up, and helped Liberty maintain as much control over the process as possible. Scout's dad was caught between dueling ideologies and unsure of whose side to take. As much as I like him, I don't think he had the life experience needed to cope with a hospital trying to force its agenda on you through scare tactics. He tended to side with the doctors more often than not, but nothing in his experience told him to have anything but faith in what a doctor recommended. Despite that, Liberty's force of will and the strong advocacy of the midwife kept the unnecessary interventions to a minimum.

To be fair to Scout's dad, when Stacey was born, I was of a similar mindset, and Stacey's mom and I thought the hospital was just where you were supposed to go for labor. It wasn't until years later that it dawned on me that doctors are normal people with their own agenda, and a healthy skepticism was needed. I also knew that people still gave birth before there were hospitals, and people were trained to assist the mother before the field of medical obstetrics was invented. It wasn't until recently that it all clicked together for me: In the 60 years that hospital birth in developed countries has been the norm, we've progressed only marginally from twilight sleep and leather straps. The medical community continues to lack empathy and support for mothers in labor, and until this changes, hospital births should be avoided where possible. The field of obstetrics has done too much to disempower and dehumanize women in what is supposed to be an important, memorable, beautiful event. Women should be revered while they're creating life; doing otherwise is God-damned unconscionable.

Back to the story: Because Liberty was induced before her body was ready, her body balked, and she endured a painful 3 day labor. Despite the long labor, the constant onslaught of doctors saying, as if scolding a small child for not cleaning her room, "you know, it's going to be time for a C-section if you don't progress soon," and despite the physical pain of prolonged use of Pitocin, Scout was born vaginally, without need of scalpel or forceps, and from what I've divined in the 3 and a half years I've known her, is both healthy and intelligent. Everything ended well with Scout's birth, but needless to say that isn't the type of birth we want this time.

We found a good midwife center here in Columbus, CHOICE, to see during the pregnancy, and we intend to have the baby on The Farm, a commune that managed to survive after the 70s when the popular hippie movement died down, and home to the mother of modern midwifery, Ina May Gaskin. Ina May authored "Spiritual Midwifery", which I can't recommend highly enough to anyone planning on having a baby, and was interviewed in Ricki Lake's movie, "The Business of Being Born", a must-see for the expecting couple. She is also the namesake of the Gaskin Maneuver, a Guatemalan technique that she popularized that helps with shoulder dystocia - where an infant's shoulder gets stuck when they crown. (When we went down to visit The Farm recently, Liberty saw Ina May driving by, and was all excited. It was cute.)

After being frank about the previous birth to our CHOICE midwife, she said some things that we were happy to hear, namely that preeclampsia is more common in first-time mothers, and a high protein, high calcium diet is good insurance against a repeat occurrence. I found some articles and a study that supported both of those assertions, which was reassuring to me. Before meeting Liberty, I had no experience with what midwives were supposed to be (as is true of most Americans). Based on my experiences so far, I'm sold on them. They are competent professionals, more knowledgeable about childbirth than the surgeons who call themselves obstetricians. Midwives believe, like I do, that childbirth doesn't belong in a hospital with medical intervention, or with the mother on her back, scared, and taking orders.

So coupled with the protein/calcium diet advice, Liberty wanted to monitor her fluid and fiber intake as well, so she set out to look for an iPhone app that could help her track all that. Sadly there weren't any that had all four, or that were customizable. And this is where I come in, using my geek mojo to try to attack the problem.

About 6 months back, I signed up for Apple's developer program, giving them my gmail address, but never heard back. My main home workstations run XP and Linux, so to use XCode to write iPhone apps, I would need to confiscate Liberty's Macbook, giving me two reasons not to code a native app right off the bat. After some digging, I found that Safari supports the offline application cache and web storage specs, and iOS lets you bookmark a website to the "desktop" with a custom icon and splash screen, and provides controls to put Safari in a sort of kiosk mode. In other words, you can click on a button on the main screen, have it open a web app that can save data locally, and the result is basically indistinguishable from a native app. With this approach, I would be able to code for the iPhone with Windows or Linux, and not pay Apple for the right to do so, so that's the road I took.

Getting started

At the beginning of this effort, I decided to code the UI from scratch using un-obfuscated JavaScript to build tables, "buttons" (<span> tags, actually), and onclick handlers. In an attempt to move things along quickly, I didn't fully separate out functionality using MVP, MVC, or other mainstream architectural patterns, but the UI and object functions are fairly split apart. To illustrate, here are functions to build a generic button (UI), and another to remove a food item from a day's eating history (object model).


function makeButton(buttonText, callBack) {
  var button = document.createElement('span');
  button.className = 'button';
  button.innerText = buttonText;
  button.onclick = callBack;
  return button;
}

function removeItem(index, dayString) {
  if (lentil[dayString] == null || lentil[dayString][index] == null) return;
  lentil[dayString].splice(index, 1);
  saveData();
}

Whereas, here is sort of a kluge to return a table of a day's eating, that can't decide if it's the user interface, the object model, or a controller:


function getDayTable(dayString) {
  var outTable = initTable();
  if (lentil[dayString] == null) lentil[dayString] = [];
  var totals = [];
  for (var n = 0; n < trackElements.length; n++) totals.push(0);

  var counts = {};
  for (var n in lentil[dayString]) {
    var name = items[lentil[dayString][n]].name;
    counts[name] = (counts[name] == null) ? 1 : counts[name] + 1;
  }

  var seen = {};
  for (var n in lentil[dayString]) {
    var itemNum = lentil[dayString][n];
    var item = items[itemNum];
    if (seen[item.name] == null) {
      roundCollection(item.elements);
      var row = collectionToCountsRow(item.name, item.elements, counts[item.name]);
      var callback = new callbackRef('verifyRemove', itemNum, n, dayString);
      row.onclick = callback.invoke;
      outTable.appendChild(row);
      incrementTotals(itemNum, totals, counts[item.name]);
      seen[item.name] = true;
    }
  }
  outTable.appendChild(totalsRow(totals));
  return outTable;
}

There's still quite a bit of overlap, and as the code progresses I'll get better role separation. Round one, though, quick and dirty, weighing in at only 400 lines of JavaScript and giving my wife something usable while she's still pregnant, a more important concern than glass-tower programming theory.

Lentil

You may have noticed references above to a hash named "lentil". When Liberty was early in her first trimester, she estimated the baby's size to be about that of a lentil. When she would have baby-related symptoms such as an upset stomach, she would say things like "Lentil is really doing a number on me today." So after she balked at my naming the first build of my program "Preggers", she recommended the name Lentil instead, which was more agreeable to both of us.

We shamelessly stole an image off the net for the home screen button:

...but we have a wooden bowl and a bag of lentils at home with which to make a similar image of our own so we won't be dirty cheaters. Or get sued.

Making a web page look like an app

There are a pair of HTML meta tags to enable fullscreen mode and darken the status bar (the top of the iPhone screen that shows your battery level, time, etc.) They are as follows:


<meta name="apple-mobile-web-app-capable" content="yes" />
<meta name="apple-mobile-web-app-status-bar-style" content="black" />

Another meta tag can change viewport settings, like disabling zooming, and setting the viewport's width and initial zoom levels:


<meta name="viewport" content="user-scalable=no, width=device-width, initial-scale=1.0, maximum-scale=1.0"/>

The last iPhone-specific HTML-based hints I used are for setting the home screen icon and the splash-screen. The addresses are relative to the location of the page they are referenced from.


<link rel="apple-touch-icon" href="images/icon.jpg"/>
<link rel="apple-touch-startup-image" href="images/startup.png" />

My splashscreen is a little cartoony right now; it's definitely something that will be professionalled-up when this comes out of beta. Here's the current image:

With those HTML tags on a page, you can visit it from Safari on the iPhone, bookmark it to your homescreen, and from then on it will open like a native app. More information about tags that will influence Safari on the iPhone are available here (as well as scores of other pages).

Offline Web applications

The W3C's HTML5 working draft has a nice summary of how offline caching of web applications works, available here. Briefly, the main HTML page references a manifest file. The manifest file lists what files to cache, and the browser caches them. The next time the page is opened, a single query to the web server is made to see if the manifest file has been altered. If it hasn't (or if the browser is offline), all the web resources are loaded from the cache instead of the network.

In other words, if I open a cached web application while the iPhone is in airplane mode, it will still open. Additionally, if the manifest file hasn't been updated, only a single HTTP GET is issued for the manifest file before the application opens, speeding up opening quite a bit.

The caveat is that the manifest file must be served with a content type of "text/cache-manifest" for browsers to turn on caching. In the near future, I imagine by default most web servers will serve .manifest files with this content type, but currently some twiddling is needed - at least, that's true on my current web server of choice, Google's App Engine.

I use Eclipse/Java for deploying App Engine projects, and changing the content type served for a given file extension is accomplished with a few lines in the project's web.xml file:


<mime-mapping>    
  <extension>manifest</extension>        
  <mime-type>text/cache-manifest</mime-type>        
</mime-mapping>

To verify this was working as expected, I deployed a project, telnetted to the web server on port 80, and did a manual GET for the file:


GET /lentil.manifest HTTP/1.1
Host: lentiltracker.appspot.com

HTTP/1.1 200 OK
ETag: "kRe4nQ"
Date: Sat, 02 Apr 2011 08:47:45 GMT
Expires: Sat, 02 Apr 2011 08:57:45 GMT
Cache-Control: public, max-age=600
Content-Type: text/cache-manifest
Server: Google Frontend
Transfer-Encoding: chunked

a3
CACHE MANIFEST

# Beta 9.

# js files
json2.js
lentil.js
...rest of file
0

As you can see, the content type came through correctly. Rather than the browser downloading the entire file each time and comparing it with a cached copy, the HTTP entity tag reference (ETag) is used to determine if the web server thinks the file has changed. This is accomplished by including an "If-None-Match" field in the GET request, specifying the last ETag value. If the browser gets back an HTTP 304 response, it knows there's no need to re-download the entire file. Here's how that looks over telnet:


GET /lentil.manifest HTTP/1.1
Host: lentiltracker.appspot.com
If-None-Match: "kRe4nQ"

HTTP/1.1 304 Not Modified
ETag: "kRe4nQ"
Date: Sat, 02 Apr 2011 08:53:31 GMT
Server: Google Frontend

My project has a number of resource files with it: The main HTML page, a CSS file, JavaScript file, the icon and splashscreen images, and of course the manifest file. My App Engine resource usage will look something like this for requests that come after all of those files have been cached:

Ideally, just the manifest file, and most of those should be HTTP 304s. What I've found in practice, though, is that App Engine gives the occasional HTTP 200 for a file that hasn't changed, which leads me to believe they don't always store the ETag field the same way on all mirrored servers, or possibly each App instance regenerates new values. Consequently, Safari busies itself with comparing the file contents, and sees that all is well so doesn't re-download the CSS, JavaScript or main page files. In some of these cases, the iPhone's desktop subsystem will re-download the icon and splashscreen files, sending a user agent containing CFNetwork and Darwin, contrasted with Safari's AppleWebKit. A typical set of log entries looks like this:

Even considering that the 304s aren't consistent, this is still a lot less traffic than having each file be downloaded fresh each time the app runs. The web traffic benefit is good reason to use application caching of static content (or code) where possible, even if you aren't trying to make a web page look like a native iPhone app.

Since Safari on the iPhone and Google Chrome both use the WebKit engine, I did most of my testing for this project with Chrome on Windows for the basic reason that its debugging tools are fantastic. For example, from the chrome://net-internals/ URL, you can capture and view raw network bytes, as well as see when Chrome is grabbing a resource from the application cache instead of the network. For example, here is how Chrome responded to the order to load my app's CSS file:


Start Time: Sat Apr 02 2011 04:33:06 GMT-0400 (Eastern Daylight Time)

t=1301733186906 [st= 0] +REQUEST_ALIVE             [dt=69]
t=1301733186906 [st= 0]    +URL_REQUEST_START_JOB  [dt=29]
                            --> load_flags = 65536 (VERIFY_EV_CERT)
                            --> method = "GET"   
                            --> priority = 1     
                            --> url = "http://lentiltracker.appspot.com/lentil.css"
t=1301733186916 [st=10]        APPCACHE_DELIVERING_CACHED_RESPONSE  
t=1301733186935 [st=29]    -URL_REQUEST_START_JOB  
t=1301733186975 [st=69] -REQUEST_ALIVE

In fact, the net-internals page is where I first noticed the business with ETags and HTTP 304 responses:

If you want to see all the stored manifest files, or delete individual application caches, you can accomplish that from chrome://appcache-internals/, as shown in this screenshot:

Storing data locally

In the past, having a browser store data locally could only be accomplished with HTTP cookies, the much-maligned bastard stepchild of the Internet. There are two major drawbacks to using them, namely size limits (4k per cookie, 20 cookies per domain), and the fact that they are sent by the client with every request. The original Netscape recommendation for cookies indicated the idea was for them to manage "state". The server would be notified what state the browser thought it was in, and the server could make decisions based on that.

A newer recommendation for web storage is being hashed out for the HTML5 standard, and Chrome and Safari (and I assume other browsers) already have it implemented, complete with a handy JavaScript accessor: localStorage.[name] = [string] for storing simple strings. There is also a web database recommendation that allows local DB objects that can be queried with SQL, but I chose the simple localStorage method so I could get something functional quickly, and used JSON to turn my JavaScript objects into strings.

I ended up with a pair of simple functions that manage turning an eating history object and a food types object into localStorage strings, and back again:


var lentil = {}; // History hash
var items = [];  // Array of food types

function init() {
  if (localStorage == null) {
    alert("Local storage features won't work in this browser.");
  } else {
    if (localStorage.lentilHistory) lentil = JSON.parse(localStorage.lentilHistory);
    if (localStorage.lentilItems) items = JSON.parse(localStorage.lentilItems);
  }
}

function saveData() {
  localStorage.lentilHistory = JSON.stringify(lentil);
  localStorage.lentilItems = JSON.stringify(items);
}

Chrome's developer tools can be used to see the raw contents of the local storage DOM tree, as shown here:

Now that I have my feet under me with web apps, I can either databasify this, or at least split foods and days into unique objects so that the entire history can't be blown away with one bad write. How to manage doing that and save all the data Liberty already has entered will take some hemming and hawing, but shouldn't be too much of a puzzler.

The rest is all JavaScript to handle events and turn arrays of food items into tables. Here are a few screenshots of how the pages look now, but it needs a little usability tweaking, and a lot of prettying up.

More tweaks of the app will come, and in all likelihood I'll leave it up on the App Engine page as a free tool. The end result that I care about, though, is Liberty's use of it. She is tracking her calcium and protein, and can see at a glance if she's on the road to avoiding a second hospital birth. As a husband who cares about this sort of thing, I'm doing everything in my power to support a natural birth. I'm just glad in this case there is enough overlap between what I'm good at and what Liberty needs so that I can contribute.

Success through embracing mistakes

2011-03-05T11:46:00.001-05:00

"The dogmas of the quiet past, are inadequate to the stormy present. The occasion is piled high with difficulty, and we must rise -- with the occasion. As our case is new, so we must think anew, and act anew. We must disenthrall ourselves, and then we shall save our country." - Abraham Lincoln

"I hate math, dad" my daughter said to me a few days ago. It wasn't really a shock to hear it, rather it was the final nail in the coffin, which I'd seen coming for the last few years. The middle school years, sitting in rows, staring at the backs of her peers' heads, listening to lectures, seeing story problems which were so fanciful as to be ridiculous. So Bill's dad's age is 5 less than 3 times Bill's age, and the sum of their ages is 49? Really? Does that sort of thing come up in life a lot?

As a toddler, we played with shapes and numbers for fun. I showed her how fractions work at 4 years old, by drawing on my whiteboard at the office. I drew a circle and drew lines through it, then shaded parts in and wrote down the fraction it represented. With some experimentation, she saw how shading two quarters of a circle took up the same space as one half. She "got it", and was thrilled to figure out fractions. Innoculated against the idea that math is hard, she spent all of her elementary school years scoring off the charts in math, and was offered a spot in an advanced math/science program in the 4th and 5th grades, going to a different school once a week to work solely on math and science topics.

And then there was middle school. Now in high school, with the middle school craziness coupled with years of peer pressure to reject appearing smart in order to be more popular, her standardized test scores slipped from "phenomenal" to merely "advanced". The coup de grâce happened this year, when she told me flatly how she feels about math. Another creative spirit successfully crushed by an education system designed in the 19th century to meet the needs of industrialism.

Something similar happened to me, back in the day. One of the reasons that I didn't go to college is that traditional education doesn't agree with me. In school I learned many strategies for test-taking that did not involve learning the subject matter of the class. I felt stifled by the needless repetition of lessons. I dislike the overall layout of textbooks, and the transparent committee thinking that goes into them.

What I disliked the most, though, was the idea that mistakes were bad, and not a tool for learning. A test would have, say, 20 questions on a chapter's topic, and you would have 20 chances to make a mistake that would cost you points. In classes where I "got it" to the point of being bored and wanting to move on, the repetition would get me. By question 5 I'd be hurrying through the uninteresting test and making speed-based errors rather than mistakes based on not knowing the material. In classes where I didn't "get it", the opposite behavior of going slower and using test-taking strategies artificially inflated my test scores, and made it seem that I knew material that I didn't.

Somehow I managed to come out of school with a love of numbers, and of science, history, and books, but all of that was at risk of being crushed by traditional schooling. For me it was a close shave with rejecting all academics, as I was more focused on passing tests and getting the hell away from school than I was in embracing what was being taught. It was a lot of effort to find the tiny nuggets of "interesting" buried in the rubble of textbooks and lesson plans, but I eventually found them. My high school helped when I was on the brink of throwing it all away. I went to the Linworth Alternative Program, whose teachers were much easier to cope with. The AP was a much better approach to education than I had seen in the seven schools I had been to previously, but even they were subjected to the tyranny of test = grade.

The running theme that school threw at both my daughter and myself is this: Pass the test. The more mistakes you make, the worse you "do" in the class, regardless of what skills you learn. Measuring knowledge or understanding is not happening, only test-taking ability is being measured. To prepare for a test, one crams, regurgitates, and forgets. Next year, the teacher has to re-explain the basics supposedly learned the previous year before starting any new material.

Outside of schools, making mistakes is a tool that increases your understanding of the world around you. When learning a new skill, you will be very error-prone at first as your brain and body try to cope with something they have never done before. When you first learn to play the piano, you can't make it through a piece error-free to save your life. Eventually the smaller skills that make a musician get mastered: sight-reading music, hand separation, hearing the piece in your head, finger strength and speed, passion.

Any junior level software developer tasked with solving a new problem will tell you this story: "I took the problem statement and started coding for it. Once I figured out what I was doing wrong, I better understood the nature of the problem. Then I started over and wrote a better program." A more advanced developer will tell you the real value of tests is in failing them. In fact, the Test Driven Development model is exactly that: Write a test for the requirement before you write any code, a test that is guaranteed to fail out of the gate. Run the test and watch it fail. (If it doesn't fail, your test is flawed). Code for the new test, then run all the tests again, until nothing fails. (There's more to it than that outside the scope of this screed, and if you're interested you can get more info here.)

In my job, tests are for tuning functionality, and if you don't fail a bunch of tests in the process of writing your program, you're either a damned genius or you're writing something simplistic and boring. In school, tests immediately serve to bring down your grade in the class, so the students must concentrate not on learning skills, but on passing tests. Will this be on the test? What's the answer the teacher wants?

This is all ass-backwards on its face, and judging by my daughter Stacey's experiences 20 years after my own, schools are still being run the same way. There is advocacy for change, by the likes of Dan Meyer and Ken Robinson, but change is slow in coming.

My solution? Grade all classes the way arts classes are graded, with the three Ps: Participation, passion, and projects. In drama class, a play can demonstrate the skills of memorization, timing, getting into character. In drawing classes, projects can demonstrate understanding of perspective, observation, different mediums.

In math classes, is it important that students can calculate by rote dozens of times in a row? No, unless they are yearning for assembly line work. Instead, how about projects demonstrating the desired skills? Look for a real life problem that can be measured and have math principles applied to it. Mom and Dad each have cars with different MPGs, and they work different distances from home. How can they save gas? Dad's credit cards are maxed out, and he has $40 extra dollars a month dedicated to paying them off. Each card has a different balance and interest rate. In what order should he apply the $40 to pay them off the quickest?

Math class would be the easiest to reform, since I think everyone would agree it's the most broken. Other classes would be harder (by me, anyway) to modernize, but I believe similar project-based approaches are possible for them as well. I also believe schools should no longer be aligned with the needs of the business world. They should export thinkers, not workers. Businesses can take care of their own needs, and will find other ways to make drones when they no longer have the explicit consent of public education.

4,046

2011-01-21T07:42:00.001-05:00

I've disabled this blog's Google Analytics feed. The feed assures me that there were 4,046 visits here over the past year, most of which occurred after a swell of visits in August '10 when I started posting about various coding experiments I was working on. From that time forward, there were over 100 visits per week to the site, most of which turned out not to be loyal fans, but rather one time visits referred here by search engines.

It turns out that Google was ranking me fairly high on some search terms, and when I noticed the increased traffic, I tried to leverage that a couple different ways. First, I succumbed briefly to temptation and put Adwords advertisements on the site for a couple weeks. Now, 4,046 is a nice number for a lone blogger who started out just writing about his kid, but it's not enough to pay the bills on click-throughs. So I took them down when my Adwords balance slowly crawled to the 7 cent mark.

Next, I put up a couple different attempts to solicit feedback from visitors, which was about as popular with visitors as the ads. I got a total of 4 responses, one of which was just a smartass comment from a friend I work with, another was not honest feedback, but a solicitation to help grow a content farm.

So I've taken down the "feedback" link, and turned off analytics, as it never really bought me anything other than some nebulous insight into what people search for, and how hard it is to get the attention of people looking for homework help, job interview answers, or instructions on gaming Facebook's PuzzleMaster coding puzzles... not that I look down on any of that. If you see how I solved a problem, maybe something will click and you'll be better off. If your goal is to cheat an assignment or test, well, good luck with that, but I doubt I'm improving anyone's chances of passing a class they weren't meant to. For now, "The Sky" is back to being just a plain old blog, where I write about whatever suits me, and visitors are welcome, but not the focus.

Before turning off analytics, my most popular pages were:

"Quest for Interesting" is a whimsical post that became popular only because it contains an image I created in MS Paint in about 10 minutes, which shows how to cross-multiply to compare fractions. For whatever reason, that image was for a few months the number one hit on Google Images for "cross multiplication". It currently fluctuates between 2nd and 3rd place, and still drives traffic here.

"Solving the Facebook Gattaca Puzzle" is one of my solutions to a Facebook puzzle on their "careers" page. They use interesting puzzles involving optimization and datasets as a filtering tool for potential coders, which I think is a good idea. The number of people attempting to use search engines to game the system is phenomenal. To illustrate, here are the top 5 search terms used to find any page on my site:

"Oldschool Mainframe/COBOL geek-out" is me going on at length about mainframe topics like RPF scripts in ROSCOE, compiling and linking from JCL, why EBCDIC is even a thing, and how no one "plays" on mainframes.

The last, "Creating an Archimedean Spiral generator in Java using the NetBeans IDE" is one of several quick hacks of mine, this one attempting to be a basic introduction to using NetBeans, the basics of painting and the Java2D library, and polar math vs. Euclidean. Because it's fun. And I'm a geek who despairs not taking Calculus in high school, and not paying more attention in the math classes I did take.

So, I have dismissed my Joab from his census-taking duties, before being punished by the almighty for my pride. Now it's back to just writing about stuff, without the marketing angle.

OSU Math Placement B-test, 1 of ???

2011-01-16T10:16:00.003-05:00

A little experiment with Google Docs, Wikipedia's TeX engine for rendering math equations, and trying to help my wife pass her college math requirements.

Where's that Check 21 2 of 2 I promised for yesterday? Still coming, I just need to get my inspiration back after a few, um, let's call them "challenging" weeks at my day job. Anyway, enjoy!

B Test study guide, question 1a

Adventures in Barretting

2011-01-09T18:21:00.001-05:00

In an attempt to be funny, I made up the term “Barretting” to describe the act of driving to Tennessee to see my friend Chris Barrett. My wife, Liberty, and I had some fun throughout the week using the term whenever it would fit. “Well, we don’t need to stop at the store on Friday, we can get to that when we’re back from Barretting.”

Chris introduced us to the “Flying Saucer” pub last year, which has a giant wall full of taps (possibly 20 or 30), as well as friendly wait-staff, not too intolerable prices, and a 100-beer tour that gets you some sort of free party there and your name on a plate if you finish it. Liberty and I went once with Chris to the Memphis location, and have been twice to the one in Nashville while taking an impromptu “let’s see where this road takes us” vacation.

Chris used to live in Columbus like we do, but now works in western North Carolina. Nashville is a good midpoint between us, so we planned to meet up this weekend and catch up for a few hours, and go our separate ways. We did so, adding beers 10 through 12 to our tours (16 to 18 for Chris) and a good time was had by all. But something happened on the way down that trumps that story.

On Saturday morning we started our drive down, and by mid-afternoon, with the sun starting to dip low in preparation for nightfall, we found ourselves on I-65, a little South of Louisville Kentucky. There was this idyllic moment as we drove down a stretch of road with rock structures on either side. There were a couple clouds visible, contrasting the darkening blue sky, a flock of birds crossed the road in front of us, first horizontal, then swirling to a vertical diamond-shape as the crossed the opposite rock facing. Liberty was sitting beside me, engrossed in knitting a new creation, and a local radio station was playing the Zeppelin song “In My Time of Dying”.

And there it was. Our life and responsibilities back home - to kids, house, school, and job - was a fiction that neither of us believed in. The truth was the road, the song, the shawl, the birds, and the setting sun. And the real truth: each other.

I felt a sense of overwhelming bliss just driving around with the woman I love. No matter what happened after we decided our fiction back home was real again, Liberty would be with me still, and hence, the world would be less bleak.

In 71 days we will have been married for three years. When we look at each other, we both know we found the right person. The house may collapse, my job may give me the boot, the mounting school debt may be a beast difficult to slay, but that will all be illusion. The real world will continue to be the birds serenading us before sunset, as we head down the road together.

Check 21 Java app - 1 of 2

2010-12-28T21:21:00.000-05:00

Extracting data and images from Image Cash Letter files

Background

There are many terms relating to Image Cash Letter files: Check 21, DSTU X9.37, X9.100-187, and check truncation, to name a few.

"Check 21" refers to an act passed in 2003. From Wikipedia's "Check 21 Act" article:

The Check Clearing for the 21st Century Act (or Check 21 Act) is a United States federal law, Pub.L. 108-100 ... The law allows the recipient of the original paper check to create a digital version of the original check—called a "substitute check," thereby eliminating the need for further handling of the physical document...
...Recently, Check 21 software providers have developed a "Virtual Check 21" system which allows online and offline merchants to create and submit demand draft documents to the bank of deposit. This process which combines remotely created checks (RCC) and Check 21 X9.37 files enables merchants to benefit from direct merchant-to-bank relationships, lower NSFs, and lower chargebacks.

The last paragraph bears some resemblance to reality, but the article's footnote refers to just one of many companies capitalizing on the Check 21 act, and the lofty goal of direct merchant-to-bank relationships is not met due to the very fact of requiring a middle-man's software to manage the relationship.

The text of the act itself is available at this page on gpo.gov, the opening paragraph being:

To facilitate check truncation by authorizing substitute checks, to foster innovation in the check collection system without mandating receipt of checks in electronic form, and to improve the overall efficiency of the Nation's payments system, and for other purposes.

My interpretation is that the act clearly states that no one is forcing banks to receive checks electronically, but new law is being written allowing banks to use electronic copies (or photocopies, or re-prints) of checks in place of the originals at their discretion. Later text in the act provides for a future study to see how banks are adopting it, whether their profits are affected, whether it's useful, etc.

When the act was passed, ANSI published DSTU X9.37 "for Electronic Exchange of Check and Image Data". "DSTU" stands for "Draft Standard for Trial Use". "X9" is the banking arm of ANSI (where "X12" is the EDI arm). So basically in 2003 a trial standard was published for exchanging check images, with an evaluation of the standard to come later. That came in 2008, when ANSI published X9.100-180 for Canadian use, and X9.100-187 for use in the states, with minor alterations from the original standard.

Background on the file format

An image cash letter is designed for mainframe use. It is record-based, with a 4-byte word at the beginning of each record indicating its length. It contains mixed text and image data, with the text part being in the EBCDIC character set, and the image part being TIFF data. If you are a small business that happens to have a mainframe laying around, this is good news. For merchants living in the real world, not so much.

The file format poses a number of challenges for Windows, Mac, and Unix programmers. Unless you are versed in the mainframe/AS400 world, variable length records with length bytes and the EBCDIC character set are probably unfamiliar to you. Once you figure out EBCDIC translation, you then need to tackle converting the record-length header to a number, which, unless you are in the habit of programming at a "bits on the wire" level (checksums, for instance), you've probably never needed to do before.

Once you tackle record lengths and EBCDIC and start playing with the image data, you'll quickly realize a simple fact that you never noticed before: nothing supports TIFF images. Your web browser doesn't display them, and your programming language doesn't have support for them in its native image library. You either need to invest more research time into finding a TIFF library and learning its API, or just dump image data to individual files each time you come across it, leaving your end-user with a large collection of files to open by hand. This would lead to the following uncomfortable conversation:

User: "So I'll have a bunch of image files representing checks that I have to click on one at a time to view?"
You: "Right."
User: "And there's no way to correlate those back to the text data?"
You: "Right."
User: "Well, do I at least get the front and back of checks in the same image?"
You: "Um, well... no."

Because of these mild but unfamiliar technical hurdles, the third-party app that supports Check21 files looks more attractive to a CTO than watching the internal IT team bumble around trying to build an app. In fact, an industry has popped up around these files, costing companies money in vendor lock-in that they tried to save by converting from ACH files and mailing checks, all in the name of getting money to the bank a little faster. Not a good situation.

Impetus for this entry

In July of '09, I published a perl script that does just what I described above. It takes a Check 21 file and prints its ASCII-translated text to STDOUT, and saves the image data into individual TIFF files. It was intended only as a quick experiment with handling the Check21 file format, but its Google rank grew until it was on the front page for searches like "x9.37 parse". This is odd because the script is a quick hack (in fact the first comment on it complains about its lack of exception handling) that I threw together in about 30 minutes, so it's possible that there aren't many "open" apps available that handle this file type.

Recently someone asked me for help with a problem using the extractor. Between my script's unexpected high search rank, and the fact that questions about my tech posts are pretty rare, one can reasonably assume that Check21 files are currently a big deal in "the wild", and knowledge about them is pretty slim. Assuming that to be the case, this post is the first in a two-part Check21 java series exploring the file format, and concerns with parsing, displaying, and creating Check21 files. This first post shows how to write an extractor similar to my perl script, but in Java.

Bits on the wire

Let's start by opening a file in a hex editor to see what it looks like. The file I'm using is available on this page on x937.com, a private site run by software developer Norman Graham.

To the untrained eye, this looks like so much garbage. To those more mainframe-savvy, the top section peppered with at-signs and letters with diacritics means you're probably looking at EBCDIC rendered with an ASCII viewer. To the image geeks, the II* on line 210h is indicative of the beginning of TIFF data.

The first four bytes combine as one hex number: 0x00000050, or decimal 80, meaning the next 80 bytes constitute a record. The next few bytes (F0, F1, F0, F3) are EBCDIC representations of numeric digits, as EBCDIC places 0 through 9 in hex F0 through hex F9 (where ASCII has them at hex 30 through 39), so the first four characters of the record should be "0103".

Tracing through the JRE

With those basic assumptions, let's throw some code at it and see what we get. The record length header can be turned into a number with very little effort. The Java class javax.imageio.stream.ImageInputStreamImpl provides the following method:


public int readInt() throws IOException {
    if (read(byteBuf, 0, 4) < 0) {
    throw new EOFException();
    }

    if (byteOrder == ByteOrder.BIG_ENDIAN) {
        return
            (((byteBuf[0] & 0xff) << 24) | ((byteBuf[1] & 0xff) << 16) |
             ((byteBuf[2] & 0xff) <<  8) | ((byteBuf[3] & 0xff) <<  0));
    } else {
        return
            (((byteBuf[3] & 0xff) << 24) | ((byteBuf[2] & 0xff) << 16) |
             ((byteBuf[1] & 0xff) <<  8) | ((byteBuf[0] & 0xff) <<  0));
    }
}

The variable "byteBuf" is a byte array. Four bytes are read into it, and using bitwise math, a single 32-bit integer is returned. This is a less processor heavy version of looping through the byte array, multiplying by 256, and adding the next byte.

So if I open the file as an ImageInputStream, I can use readInt() to grab record lengths and move forward in the file. Next, the EBCDIC to ASCII translation. The java.lang.String class has a constructor that accepts a string input declaring the character set:

public String(byte bytes[], String charsetName)

This is ultimately a convenience method for java.lang.StringCoding.decode(), which looks up a CharSet class and returns a new String by converting each byte using a translation table. For EBCDIC translation, specify "Cp1047" as the character set name, and Java will find the class sun.nio.cs.ext.IBM1047, which contains this table:


 private final static String byteToCharTable =
 
     "\u00D8\u0061\u0062\u0063\u0064\u0065\u0066\u0067" +     // 0x80 - 0x87
     "\u0068\u0069\u00AB\u00BB\u00F0\u00FD\u00FE\u00B1" +     // 0x88 - 0x8F
     "\u00B0\u006A\u006B\u006C\u006D\u006E\u006F\u0070" +     // 0x90 - 0x97
     "\u0071\u0072\u00AA\u00BA\u00E6\u00B8\u00C6\u00A4" +     // 0x98 - 0x9F
     "\u00B5\u007E\u0073\u0074\u0075\u0076\u0077\u0078" +     // 0xA0 - 0xA7
     "\u0079\u007A\u00A1\u00BF\u00D0\u005B\u00DE\u00AE" +     // 0xA8 - 0xAF
     "\u00AC\u00A3\u00A5\u00B7\u00A9\u00A7\u00B6\u00BC" +     // 0xB0 - 0xB7
     "\u00BD\u00BE\u00DD\u00A8\u00AF\u005D\u00B4\u00D7" +     // 0xB8 - 0xBF
     "\u007B\u0041\u0042\u0043\u0044\u0045\u0046\u0047" +     // 0xC0 - 0xC7
     "\u0048\u0049\u00AD\u00F4\u00F6\u00F2\u00F3\u00F5" +     // 0xC8 - 0xCF
     "\u007D\u004A\u004B\u004C\u004D\u004E\u004F\u0050" +     // 0xD0 - 0xD7
     "\u0051\u0052\u00B9\u00FB\u00FC\u00F9\u00FA\u00FF" +     // 0xD8 - 0xDF
     "\\\u00F7\u0053\u0054\u0055\u0056\u0057\u0058" +     // 0xE0 - 0xE7
     "\u0059\u005A\u00B2\u00D4\u00D6\u00D2\u00D3\u00D5" +     // 0xE8 - 0xEF
     "\u0030\u0031\u0032\u0033\u0034\u0035\u0036\u0037" +     // 0xF0 - 0xF7
     "\u0038\u0039\u00B3\u00DB\u00DC\u00D9\u00DA\u009F" +     // 0xF8 - 0xFF
     "\u0000\u0001\u0002\u0003\u009C\t\u0086\u007F" +     // 0x00 - 0x07
     "\u0097\u008D\u008E\u000B\f\r\u000E\u000F" +     // 0x08 - 0x0F
     "\u0010\u0011\u0012\u0013\u009D\n\b\u0087" +     // 0x10 - 0x17
     "\u0018\u0019\u0092\u008F\u001C\u001D\u001E\u001F" +     // 0x18 - 0x1F
     "\u0080\u0081\u0082\u0083\u0084\u0085\u0017\u001B" +     // 0x20 - 0x27
     "\u0088\u0089\u008A\u008B\u008C\u0005\u0006\u0007" +     // 0x28 - 0x2F
     "\u0090\u0091\u0016\u0093\u0094\u0095\u0096\u0004" +     // 0x30 - 0x37
     "\u0098\u0099\u009A\u009B\u0014\u0015\u009E\u001A" +     // 0x38 - 0x3F
     "\u0020\u00A0\u00E2\u00E4\u00E0\u00E1\u00E3\u00E5" +     // 0x40 - 0x47
     "\u00E7\u00F1\u00A2\u002E\u003C\u0028\u002B\u007C" +     // 0x48 - 0x4F
     "\u0026\u00E9\u00EA\u00EB\u00E8\u00ED\u00EE\u00EF" +     // 0x50 - 0x57
     "\u00EC\u00DF\u0021\u0024\u002A\u0029\u003B\u005E" +     // 0x58 - 0x5F
     "\u002D\u002F\u00C2\u00C4\u00C0\u00C1\u00C3\u00C5" +     // 0x60 - 0x67
     "\u00C7\u00D1\u00A6\u002C\u0025\u005F\u003E\u003F" +     // 0x68 - 0x6F
     "\u00F8\u00C9\u00CA\u00CB\u00C8\u00CD\u00CE\u00CF" +     // 0x70 - 0x77
     "\u00CC\u0060\u003A\u0023\u0040\'\u003D\"";     // 0x78 - 0x7F

Client code

Here is a quick test class to open the file as an ImageInputStream, and attempt to find the first record's length, read that many bytes, and translate to ASCII.


package com.cea.check21;

import java.io.File;
import java.io.IOException;
import javax.imageio.stream.FileImageInputStream;

public class Test {
  public static void main(String[] args) throws IOException {
    FileImageInputStream is = new FileImageInputStream(new File("one.x9"));
    int recLen = is.readInt();
    System.out.println("Record length: " + recLen);
    byte[] rec = new byte[recLen];
    is.read(rec);
    System.out.println(new String(rec, "Cp1047"));
    is.close();
  }
}

After running that, the following output is displayed:


Record length: 80
0103T113000609111012822200408052030NUS BANKO NORM     First Bank of NormAUS

This looks good. 80 matches the record length we calculated from the hex dump, and the first four characters are "0103" as we expected. The rest of the line looks like numbers and semi-readable text, so we're definitely on the right track.

Now let's flesh out the class a little by iterating over each record and see what happens. The new class:


package com.cea.check21;

import java.io.File;
import java.io.IOException;
import javax.imageio.stream.FileImageInputStream;

public class Test {
  public static void main(String[] args) throws IOException {
    FileImageInputStream is = new FileImageInputStream(new File("one.x9"));
    int recLen;
    while ((recLen = is.readInt()) > 0) {
      System.out.println("Record length: " + recLen);
      byte[] rec = new byte[recLen];
      is.read(rec);
      System.out.println(new String(rec, "Cp1047"));
    }
    is.close();
  }
}

The output:

...and finally:


Exception in thread "main" java.io.EOFException
 at javax.imageio.stream.ImageInputStreamImpl.readInt(ImageInputStreamImpl.java:237)
 at com.cea.check21.Test.main(Test.java:11)

OK, so a closer inspection of the API would have shown that readInt() throws an exception when it reads past the end of the file, but other than that, we're good up to the point where the image data is encountered. The image data occurs where the spec says it will: on the 52 record, at column 118.

So to finish up text conversion, we need to do two things. First, handle EOF more gracefully, and second, print only the first 117 characters of 52 records.


package com.cea.check21;

import java.io.File;
import java.io.IOException;
import javax.imageio.stream.FileImageInputStream;

public class Test {
  public static void main(String[] args) throws IOException {
    File file = new File("one.x9");
    FileImageInputStream is = new FileImageInputStream(file);
    
    while (is.getStreamPosition() < file.length()) {
      int recLen = is.readInt();
      byte[] rec = new byte[recLen];
      is.read(rec);
      String recNum = new String(rec, 0, 2, "Cp1047");
      if (recNum.equals("52")) System.out.println(new String(rec, 0, 117, "Cp1047"));
      else System.out.println(new String(rec, "Cp1047"));
    }
    is.close();
  }
}

Which outputs:


0103T113000609111012822200408052030NUS BANKO NORM     First Bank of NormAUS     
100111300060911101282220060109200601092030FG16410001nfg MANAGEMENTxxxxxxxxxxC0  
200109100002211101282220070315200703150020300001000104053000196                 
25           1104 113000609    123456789012345/00000004320999987267040  G01Y000 
50111101282220060109000002206260000                     0                       
5211101282220060109040991400001                                                 
    0                0000000000018628
50111101282220060109000002206261000                     0                       
5211101282220060109040991400001                                                 
    0                0000000000023720
70000100000000043200000000043200001                                             
900000010000000100000000000432000000001 l NORMPOINTE BANK20060109               
9900000100000001000000010000000000000432NORMAN AGEMENT2145085900

Success!

The last step for a simple extractor is to dump TIFF data into files. We'll iterate a counter for each 52 record, and name the files img(count).tiff. Additionally, I've added some handling for specifying file names on the commandline, and finding their working directories. Lastly the class name has been changed to something more descriptive than "Test".

The final code:


package com.cea.check21;


import java.io.File;
import java.io.IOException;

import javax.imageio.stream.FileImageInputStream;
import javax.imageio.stream.FileImageOutputStream;

public class Extractor {
  public static void main(String[] args) throws IOException {
    
    if (args.length < 1) {
      System.out.println("Usage: java Extractor <checkImageFile>");
      System.exit(0);
    }
    
    File file = new File(args[0]);
    FileImageInputStream is = new FileImageInputStream(file);
    int tiffCount = 0;
    String workDir = file.getParent();
    if (workDir == null) workDir = ".";
    String sep = File.separator;
    
    while(is.getStreamPosition() < file.length()) {
      int recLen = is.readInt();
      byte[] rec = new byte[recLen];
      is.read(rec);
      String recNum = new String(rec, 0, 2, "Cp1047");
      if (recNum.equals("52")) {
        System.out.println(new String(rec, 0, 117, "Cp1047"));
        tiffCount++;
        String numberPart = String.valueOf(tiffCount);
        while (numberPart.length() < 4) numberPart = "0" + numberPart;
        String fileName = workDir + sep + "img" + numberPart + ".tiff";
        FileImageOutputStream out = new FileImageOutputStream(new File(fileName));
        out.write(rec, 117, rec.length - 117);
        out.close();
      } else System.out.println(new String(rec, "Cp1047"));
    }
    is.close();
  }
}

The text output is the same, and two image files are created in the directory containing one.x9:

And they look like this:

Next steps

This Java class is useful only so far as exploring the Check 21 file format, but provides very little real-world utility. What's needed is an app that can display check information more intelligently, including breaking down the record information into something meaningful, and displaying the front and back of a check alongside that information.

To do that, we'll need to figure out how to turn TIFF data into a Java Image object, and to explore the X9.100-187 record layouts in a little more detail.

I'm giving myself an arbitrary deadline of January 15, 2011 to post my progress with that app. Tune in then!

Java greyscale conversion

2010-12-16T18:29:00.005-05:00

Using Java, how do you convert a color image to greyscale? The most straightforward answer I've found was on Code Beach, and is as follows:


BufferedImage image = new BufferedImage(width, height,  
    BufferedImage.TYPE_BYTE_GRAY);  
Graphics g = image.getGraphics();  
g.drawImage(colorImage, 0, 0, null);  
g.dispose();

Create a BufferedImage of type TYPE_BYTE_GRAY, and grab its Graphics object. Draw the color image onto it. Fin.

The described method uses a small amount of client code for a fast, good quality greyscale conversion, but a lot goes on under the hood to make this happen in the Java runtime jar. Tracing through the code, eventually you arrive at the getDataElements method of java.awt.image.IndexColorModel, and the following line is executed over every pixel in the image:


int gray = (int) (red*77 + green*150 + blue*29 + 128)/256;

This takes the red, green, and blue components of a pixel's composite color, and calculates its relative brightness (on a scale here that is, oddly, between 0.5 and 1.5), and later uses this value to mix a grey color of the same brightness for the replacement pixel.

A quick (and admittedly non-expert) course on color theory as it relates to computers:

Your computer screen does not have pixels that can change color. For every perceived pixel, there are three "lights" (for simplicity's sake) very close together that are the primary colors red, green, and blue. When all three lights are off, you see black. When they are all turned on at full brightness, you see white. Mixing the lights at different power levels produces very close to the full range of colors that our eyes can perceive.

The lights have 256 power levels, for a total color space of 16,777,216 colors (256 cubed). Black is seen when red, green, and blue are all 0; white when they are all 255. There are also 254 shades of grey, seen when the red, green, and blue values all match and are between 1 and 254. This brings us back to the brightness equation above: find a color's brightness, scale it between 0 and 255, and you can make a grey with the same brightness by setting the red, green, and blue of the pixel to that value. Repeat for all the pixels in an image and you have a greyscale copy of it.

Whence the 77/150/29 ratio?

In 1982, when I was 11 years old and a holy terror on my 6th grade teachers, the International Telecommunication Union published Recommendation 601 for transmitting video signals digitally. In it the following luminance (brightness) equation is mentioned in section 2.1:


E'_Y = 0.299 E'_R + 0.587 E'_G + 0.114 E'_B

These numbers add up to 1, where 77, 150, and 29 add up to 256. Dividing each of those by 256 gives a close approximation to the Rec 601 ratios, with the added benefit of using only integers and dividing by a power of 2, which computer processors are very good at. These specific ratios of red, green, and blue to determine luminance can be traced back to the XYZ color space, created by the International Commission on Illumination (CIE) in 1931, which in turn references work by James Clerk Maxwell (Experiments on colour, as perceived by the eye, with remarks on colour-blindness [1855]) which itself references work done by none other than Isaac Newton in the book Opticks (1704) which talks about breaking light into its component parts using prisms, discussing compound vs. homogeneal light, building lenses and telescopes, etc.

I won't attempt a full analysis of all these works to trace the source of the numbers, but suffice to say in the 19th century, people stared at colored lights and twisted knobs to match colors, and scientists wrote down the final settings. After some math and repeated experiments, it was determined that green light looks pretty damned bright to us, red a little less, and blue less than that.

Are there better ratios to create a crisper greyscale image?

In 1993, the ITU published Rec 709, a standard for modern HDTV systems. In section 4.2, the recommended luminance formula for the 1250/50/2:1 scanning standard used the old Rec 601 values. For 1125/60/2:1 (1080i) scanning, new values are recommended:


E'_Y = 0.2126 E'_R + 0.7152 E'_G + 0.0722 E'_B

That section's footnote says "The coefficients for the equations have been calculated following the rules laid down in SMPTE RP177-1993." This refers to a 1993 publication called "Derivation of Basic Television Color Equations" by the Society of Motion Picture and Television Engineers.

...and for the low cost of $50, I can buy the paper and see what their math was. From what I gather from other sources, the new calculations change when Gamma levels are applied, with the result being values better lined up with the 1931 XYZ color space. Finding out more isn't worth $50 to me. Some hoodoo is done with the gamma to produce a better luminance value - I'll take their word for it.

Can I use the new values to greyscale an image in Java.

Yes. Instead of using Graphics.drawImage and letting Java figure out what to do with the pixels, you have to get your hands a little dirtier and work with PixelGrabbers, bitwise operators and integer arrays. But it turns out to not be that difficult.

Colors are defined in Java as 32-bit integers in four octets: alpha(opacity), red, green, and blue. For example, 0xff007f00 would be an opaque hunter-green, with the alpha set to ff(255) and the green set to 7f(127), with red and blue at 0. To take this integer value and pull out only the green part, you can either create a Color object and call its getGreen() method, or not waste the construction overhead and just do the math: right-shift 8 bits, then bitwise "and" the value to 0xff to zero out all but the last octet, with a statement like this:


int g = (color >>  8) & 0xff;

Getting the red value is similar, just bitshift 16 places instead 8, and with blue no bitshift is needed, just the bitwise "and".


int r = (color >> 16) & 0xff;
int g = (color >>  8) & 0xff;
int b = (color      ) & 0xff;

These values can then be used to construct a luminance value by plugging them into the Rec 709 numbers:


int lum = (int) ((double)r * 0.2126 + (double)g * 0.7152 + (double)b * 0.0722);

And finally a grey can be constructed by creating an integer whose red, green, and blue values all match the luminance number. This can be done with little overhead by left-shifting and using the bitwise "or" function:


int greyColor = (lum << 16) | (lum << 8) | lum;

The sample code below is a method that can be called specifying which luminance standard to use. A PixelGrabber grabs all the RGB values and sticks them into an integer array. Then the array is iterated over, converting all the colors to matching greys, and finally updating a BufferedImage with the new pixels:


private Image greyScale(int mode, Image sourceImage) {
  double redLum, greenLum, blueLum;
  switch(mode) {
  case 601:
    redLum   = 0.299;
    greenLum = 0.587;
    blueLum  = 0.114;
    break;
  case 709:
    redLum   = 0.2126;
    greenLum = 0.7152;
    blueLum  = 0.0722;
    break;
  default: return null;
  }

  int w = sourceImage.getWidth(null);
  int h = sourceImage.getHeight(null);
  int[] pixels = new int[w * h];
  
  PixelGrabber pg = new PixelGrabber(sourceImage, 0, 0, w, h, pixels, 0, w);
  try {
    pg.grabPixels();
  } catch (InterruptedException e) {
    e.printStackTrace();
    return null;
  }

  BufferedImage greyImage = new BufferedImage(w, h, BufferedImage.TYPE_3BYTE_BGR);

  int offset = 0;
  for(int y = 0; y < h; y++) {
    for (int x = 0; x < w; x++) {
      int color = pixels[offset++];
      int r = (color >> 16) & 0xff;
      int g = (color >>  8) & 0xff;
      int b = (color      ) & 0xff;
      int lum = (int) ((double)r * redLum + (double)g * greenLum + (double)b * blueLum);
      int greyColor = (lum << 16) | (lum << 8) | lum;
      greyImage.setRGB(x, y, greyColor);
    }
  }
  return greyImage;
}

Here are a couple screengrabs from an app using this method to compare the original and greyscaled images.

First using the 601 standard:

Then the 709:

The difference is subtle, but the print on Scout's dress is a little darker and better defined in the 709 image. And with that anecdotal and completely subjective comparison, I declare the 709 formula the better of the two. On a whim, I shot Oracle an email about the IndexColorModel class using the outdated formula, showing a simple change to use the updated one:


int gray = (int) (red*55 + green*183 + blue*18 + 128)/256;

I doubt that will come to anything, but, you know, it was worth at least mentioning it to them. If I get the added bonus of my line of code in the official rt.jar, so much the better.

Roman numerals redux

2010-11-20T09:04:00.006-05:00

A simple JavaScript function to validate Roman numerals, convert them to Arabic numbers, and back again.

I checked Google Analytics this morning and noticed I've been getting a lot of hits on my October 9 entry on JavaScript Roman numeral conversion. In brief, I wrote a simple function to take a number and build its Roman numeral equivalent. While I was mulling it over this morning, I spontaneously thought of a method to validate and parse a Roman numeral and turn it back into Arabic numbers using regular expressions.

Input a Roman numeral or an integer between 1 and 3999:
Strict

Step 1: Validating

What contitutes a "valid" Roman numeral is ambiguous. For example, referring to 4 as IV instead of IIII has more of a spotty history than I imagined. The Wikipedia article on roman numerals has an interesting section on this, discussing the use of IIII on clock faces, and MDCCCC on 20th century buildings instead of MCM, and some instances of using VV to represent 10. I decided not to support VV, and to add a flag that sets whether to reject IIII, XXXX, and CCCC.

Assuming IIII, VIIII, IV, and IX are all valid, here are all the possible ones place Roman numerals:


I
II
III
IV or IIII
V
VI
VII
VIII
IX or VIIII

These can be divided into two classes: IX and IV, and everything else. If the numeral contains IX or IV, you're done with the ones place. If it doesn't contain either of those, the numeral can have a V or not followed by 0 to 4 I characters (0 to 3 if we're being strict). Expressing that concept in regular expression speak is surprisingly simple, and can be built from three basic rules. I'll describe what each rule means, for those not familiar with regex.


I[XV]  - This means 'I' followed by either 'X' or 'V'.
V?     - 0 or 1 V characters
I{0,4} - 0 to 4 I characters

Now we just need to put the optional V before the optional I's, and specify either-or to the choice types by using the pipe character, making the rule:


V?I{0,4}|I[XV]

Next, the same rule needs to be applied to the tens and hundreds places, and each rule wrapped in parentheses to keep the piped choices from interfering with each other:


(D?C{0,4}|C[MD])(L?X{0,4}|X[CL])(V?I{0,4}|I[XV])

Lastly, the thousands, and binding to the start and end of the string. The beginning of the string is marked with the carat symbol, the end with the dollar sign. There can be 0 to 3 thousands at the beginning of the string, followed by the regex above, followed by the end of the string. This makes the complete regex:


^M{0,3}(D?C{0,4}|C[MD])(L?X{0,4}|X[CL])(V?I{0,4}|I[XV])$

Step 2: Evaluating

Once we're sure the string is valid, we need to break it down into tokens and add up their values. Fortunately, every letter has a set value, and only the exceptions for subtraction notation (IX, IV, etc.) need to be worried about. Regular Expressions can help us out again, as the piped list of choices uses a first match rule. We just need a list of choices that finds the subtraction notation options before it finds the individual letters:


M|CM|D|CD|C|XC|L|XL|X|IX|V|IV|I

Note that IX and IV are found before just plain 'I'. Next, assign each list option a value, and write a function to iterate over all the matches and add up the values:


var word   = /(M|CM|D|CD|C|XC|L|XL|X|IX|V|IV|I)/g;
var value  = {I:1,IV:4,V:5,IX:9,X:10,XL:40,L:50,XC:90,C:100,CD:400,D:500,CM:900,M:1000};

function getInt(input) {
  var s = 0;
  var words = input.match(word);
  for (var i = 0; i < words.length; i++) {
    s += value[words[i]];
  }
  return s;
}

Putting it all together

Using those basic concepts, and borrowing from my previous code that built a Roman numeral based on an Arabic number, I wrote a smallish function that can take either an Arabic number or Roman numeral, and convert it to the other.

The source code:


var isInt  = /^\d+$/;
var isRom  = /^[IVXLCDM]+$/i;
var valid  = /^M{0,3}(D?C{0,4}|C[MD])(L?X{0,4}|X[CL])(V?I{0,4}|I[XV])$/;
var strict = /^M{0,3}(D?C{0,3}|C[MD])(L?X{0,3}|X[CL])(V?I{0,3}|I[XV])$/;
var word   = /(M|CM|D|CD|C|XC|L|XL|X|IX|V|IV|I)/g;
var value  = {I:1,IV:4,V:5,IX:9,X:10,XL:40,L:50,XC:90,C:100,CD:400,D:500,CM:900,M:1000};


function translate(input, isStrict) {
  if (input == null || input == "") {
    alert("Please enter a value.");
    return input;
  }

  var output;
  if (input.match(isRom)) output = getInt(input.toUpperCase(), isStrict);
  else if (input.match(isInt)) output = getRom(input);
  else alert(input + " is not a Roman numeral or integer value.");

  return output == null ? input : output;
}

function getInt(input, isStrict) {
  var matcher = isStrict ? strict : valid;
  if (input.match(matcher) == null) {
    alert(input + " is not a valid Roman numeral.");
    return;
  }

  var s = 0;
  var words = input.match(word);
  for (var i = 0; i < words.length; i++) {
    s += value[words[i]];
  }

  return s;
}

function getRom(input) {
  var num = parseInt(input, 10);

  if (num < 1 || num > 3999) {
    alert("Integer must be between 1 and 3999.");
    return;
  }

  var s = "";
  while (num >= 1000) { num -= 1000; s +=  "M"; }
  if    (num >=  900) { num -=  900; s += "CM"; }
  if    (num >=  500) { num -=  500; s +=  "D"; }
  if    (num >=  400) { num -=  400; s += "CD"; }
  while (num >=  100) { num -=  100; s +=  "C"; }
  if    (num >=   90) { num -=   90; s += "XC"; }
  if    (num >=   50) { num -=   50; s +=  "L"; }
  if    (num >=   40) { num -=   40; s += "XL"; }
  while (num >=   10) { num -=   10; s +=  "X"; }
  if    (num >=    9) { num -=    9; s += "IX"; }
  if    (num >=    5) { num -=    5; s +=  "V"; }
  if    (num >=    4) { num -=    4; s += "IV"; }
  while (num >=    1) { num -=    1; s +=  "I"; }
  return s;
}

The crazy geometry of basketball courts

2010-11-15T19:55:00.000-05:00

I saw an interesting question on dy/dan today about posing basketball-related math questions to students. One of the reader suggestions was to talk open-endedly about the geometry of the court itself, to which Dan suggested writing a program that would draw a court given two mouse clicks to denote the baseline. That sounded right up my alley, so I wrote one.

Before starting to code, I had to learn about the measurements of a basketball court, and I was a little surprised by what I found. First and foremost, every league has its own sizes for every piece of the court, most differing by a foot or less. The biggest discrepancy is with the length of the court, which is 10 feet less for high school than for NCAA and above, or about 2 running steps. Naturally the FIBA league had measurements rounded to meters where all the US leagues are rounded to feet.

A couple other things struck me as odd. First, the backboard is 4 feet from the baseline - inside the court. I always assumed it was flush with the baseline. A second bad assumption of mine was that the three-point line was a conic section, like a parabola or hyperbola. It's not. It's a semi-circle at the top, and straight lines at the bottom, like a horseshoe. The rules imply this shape, but only refer to the three-point line as an arc.

The last organized basketball game I went to was with my daughter and my mentee, and we watched the Ohio State women's team trounce an unranked opponent from the comfort of the AEP suite at the Schottenstein center. As a nod to both of them, and to the AEP mentoring program which scored me the free tickets, all the measurements below are regulation NCAA women's court measurements. And I can assure you those players are capable of shooting from further out than their ridiculously truncated three-point line. And playing with the same ball their male counterparts use: two ounces heavier and one inch more in circumference. I honestly didn't start writing this as a feminist entry; the discrepancies just upset me after I thought about them for a while. Anyway, back to the code.

Java applet to draw a court:

Source code:

package cea.demos.drawCourt;
import java.applet.Applet;
import java.awt.BasicStroke;
import java.awt.Color;
import java.awt.Graphics;
import java.awt.Graphics2D;
import java.awt.Point;
import java.awt.RenderingHints;
import java.awt.Shape;
import java.awt.Stroke;
import java.awt.event.MouseAdapter;
import java.awt.event.MouseEvent;
import java.awt.geom.AffineTransform;
import java.awt.geom.Arc2D;
import java.awt.geom.Ellipse2D;
import java.awt.geom.GeneralPath;
import java.awt.geom.Rectangle2D;


public class DrawCourt extends Applet {
  private static final long serialVersionUID = 1L;
  // Paths describing the court lines, and the bottom-most free-throw separators, which are filled in and 1' foot thick
  GeneralPath court, fill;
  Shape courtTransformed, fillTransformed; // The same shapes after an affineTransform is applied to them
  Stroke stroke; // How thick of a line to draw the court with. Most lines are 2" thick (relative to court size)
  // Applet has three draw/input modes: Getting the upper-left point, the upper-right point, and drawing the court
  enum Mode {GET_UL_POINT, GET_UR_POINT, PAINT_COURT}
  Mode mode;
  Point upperLeft;

  public void init() {
    mode = Mode.GET_UL_POINT;
    addMouseListener(new GetClick());

    // Initialize court shape object
    court = new GeneralPath();
    fill = new GeneralPath();

    // Build the court shape. Comments describe what each line is, and the rectangle, ellipse, and arc
    // objects describe the bounding rectangles of the lines
    
    // Out-of-bounds rectangle, 50' by 94'
    court.append(new Rectangle2D.Double(0, 0, 50, 94), false);
    
    // Coaching box markers, 28' from baseline, three feet long, on both sides of court 
    court.append(new Rectangle2D.Double( 0, 28, 3, 0), false);
    court.append(new Rectangle2D.Double(47, 28, 3, 0), false);
    court.append(new Rectangle2D.Double( 0, 66, 3, 0), false);
    court.append(new Rectangle2D.Double(47, 66, 3, 0), false);
    
    // Center-court line, 47' from baseline (94 / 2 = 47), all the way across court (50')
    court.append(new Rectangle2D.Double(0, 47, 50, 0), false);
    
    // Restraining circle and center circle, 2' and 6' radii from middle of center-court line
    court.append(new Ellipse2D.Double(23, 45,  4,  4), false);
    court.append(new Ellipse2D.Double(19, 41, 12, 12), false);
    
    // Back-boards and baskets
    // Back-boards are 4' inside court from baseline, centered, and 6' wide
    court.append(new Rectangle2D.Double(22,  4, 6, 0), false);
    court.append(new Rectangle2D.Double(22, 90, 6, 0), false);
    // Basket are 18" circles mounted 6" from backboard
    court.append(new Ellipse2D.Double(24.25,  4.5, 1.5, 1.5), false);
    court.append(new Ellipse2D.Double(24.25, 88.0, 1.5, 1.5), false);
    
    // NCAA women's 3-point lines are 19'9" from basket's center, until 5'3" from court's side,
    // then straight down to baseline. The rules describing court layouts are ambiguous about this,
    // but this appears to be how they're laid out in reality.
    //  top
    court.append(new Arc2D.Double(5.25, -14.5, 39.5, 39.5, 0, -180, Arc2D.OPEN), false);
    court.append(new Rectangle2D.Double( 5.25, 0, 0, 5.25), false);
    court.append(new Rectangle2D.Double(44.75, 0, 0, 5.25), false);
    // bottom
    court.append(new Arc2D.Double(5.25, 69, 39.5, 39.5, 0, 180, Arc2D.OPEN), false);
    court.append(new Rectangle2D.Double( 5.25, 88.75, 0, 5.25), false);
    court.append(new Rectangle2D.Double(44.75, 88.75, 0, 5.25), false);
    
    // "The Paint", 12' by 19' rectangle, centered and touching baseline
    court.append(new Rectangle2D.Double(19,  0, 12, 19), false);
    court.append(new Rectangle2D.Double(19, 75, 12, 19), false);
    
    // Free-throw circles, the top of The Paint (the free-throw line) is the circle's diameter
    court.append(new Ellipse2D.Double(19, 13, 12, 12), false);
    court.append(new Ellipse2D.Double(19, 69, 12, 12), false);
    
    // Free-throw bottom separators (need to be filled in), are 5' from baseline, 8" wide, 1' long
    // and adjacent to The Paint
    fill.append(new Rectangle2D.Double(19.0d - 2.0d/3, 7, 2.0d/3, 1), false);
    fill.append(new Rectangle2D.Double(31, 7, 2.0d/3, 1), false);
    fill.append(new Rectangle2D.Double(19.0d - 2.0d/3, 86, 2.0d/3, 1), false);
    fill.append(new Rectangle2D.Double(31, 86, 2.0d/3, 1), false);
    
    // Other free-throw separators, 3' between edges, also 8" wide and adjacent to The Paint,
    // but only 2" long
    // top-left
    court.append(new Rectangle2D.Double(19.0d - 2.0d/3, 11, 2.0d/3, 0), false);
    court.append(new Rectangle2D.Double(19.0d - 2.0d/3, 14.0d + 1.0d/6, 2.0d/3, 0), false);
    court.append(new Rectangle2D.Double(19.0d - 2.0d/3, 17.0d + 1.0d/3, 2.0d/3, 0), false);
    // top-right
    court.append(new Rectangle2D.Double(31, 11, 2.0d/3, 0), false);
    court.append(new Rectangle2D.Double(31, 14.0d + 1.0d/6, 2.0d/3, 0), false);
    court.append(new Rectangle2D.Double(31, 17.0d + 1.0d/3, 2.0d/3, 0), false);
    // bottom-left
    court.append(new Rectangle2D.Double(19.0d - 2.0d/3, 83, 2.0d/3, 0), false);
    court.append(new Rectangle2D.Double(19.0d - 2.0d/3, 80.0d - 1.0d/6, 2.0d/3, 0), false);
    court.append(new Rectangle2D.Double(19.0d - 2.0d/3, 77.0d - 1.0d/3, 2.0d/3, 0), false);
    // bottom-right
    court.append(new Rectangle2D.Double(31, 83, 2.0d/3, 0), false);
    court.append(new Rectangle2D.Double(31, 80.0d - 1.0d/6, 2.0d/3, 0), false);
    court.append(new Rectangle2D.Double(31, 77.0d - 1.0d/3, 2.0d/3, 0), false);
  }
  
  // This method creates transformed shapes of the court shape archetypes.
  public void scaleCourt(Point left, Point right) {
    double radians;
    if (left.x == right.x) radians = left.y < right.y ? Math.PI/2 : -Math.PI/2; // Avoid divide by 0 error
    else radians = Math.atan((float)(right.y - left.y)/(right.x - left.x));
    if (right.x < left.x)radians += Math.PI; // Fix angle if in quadrants 2 or 3

    /* "factor" bears some explanation. The default size of the court shape is 1 pixel per foot. Two points
     * on the screen are clicked, representing corners of the baseline: 50' across. So, the factor to scale the shape
     * will be the real distance between the corner points divided by the default size of 50.
     */
    float factor = (float) (left.distance(right)/50);
    stroke = new BasicStroke(factor * 2.0f / 12); // Default stroke = 2 inches relative to court size
    AffineTransform tx = new AffineTransform();
    tx.setToScale(factor, factor);
    tx.rotate(radians);
    courtTransformed = tx.createTransformedShape(court);
    fillTransformed = tx.createTransformedShape(fill);
  }
  
  public void paint(Graphics g1) {
    Graphics2D g = (Graphics2D)g1;
    g.setColor(Color.BLACK);
    switch(mode) {
    case GET_UL_POINT:
      g.drawString("Click where the upper-left corner of the court will be.", 50, 50);
      break;
    case GET_UR_POINT:
      g.fillOval(upperLeft.x - 4, upperLeft.y - 4, 8, 8);
      g.drawString("Now click where the upper-right corner should be", 50, 50);
      break;
    case PAINT_COURT:
      g.drawString("Click again to start over", 50, 50);
      g.setStroke(stroke);
      g.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON);
      g.translate(upperLeft.x, upperLeft.y);
      g.draw(courtTransformed);
      g.fill(fillTransformed);
    }
  }

  class GetClick extends MouseAdapter {
    @Override
    public void mouseClicked(MouseEvent e) {
      switch (mode) {
      case GET_UL_POINT:
        upperLeft = e.getPoint();
        mode = Mode.GET_UR_POINT;
        repaint();
        break;
      case GET_UR_POINT:
        mode = Mode.PAINT_COURT;
        scaleCourt(upperLeft, e.getPoint());
        repaint();
        break;
      case PAINT_COURT:
        mode = Mode.GET_UL_POINT;
        repaint();
      }
    }
  }
}

Jury Duty

2010-11-11T17:54:00.004-05:00

On Wednesday, when I was up walking around to limber up after reading in a chair for a few hours, I came across the bulletin board in the jury pool waiting room. The board had several local newspaper op-ed pieces on jury service that may as well have been written by a chatbot, randomly generating from a dictionary of truisms and catch-phrases. "Ten Reasons I'm Glad I Served. 1: To see the inner-workings of the law. 2: To meet new friends..." Hence this post, a gritty look at my experience being on jury duty. The management summary: my experience was interesting, but the process is flawed. Like Randy Pees used to say, "Our legal system is terrible. The only one worse than ours is everyone else's."

About two weeks prior to my reading of the platitude-laden corkboard, I received a summons in the mail to report for jury duty. I tried to get out of it by replying with a letter claiming a child-care burden, as I pick up Scout from school on Tuesdays and Thursdays so that Liberty can attend later classes on those days. I got a phone call the next day telling me basically to suck it up and make other arrangements. Conveniently, this did not prove to be an actual problem: On Tuesday we were released before 5pm, and the courthouse was closed today for Veteran's Day.

On Monday, the summons instructed me to report at 8am, an hour before any trial could conceivably start. I spent most of that hour in a hot and crowded room waiting in line with a two page questionnaire asking me, among other things, whether I knew any police officers, if I had ever seen the inside of a courtroom before, or was involved in a lawsuit or related to anyone who had. My answers -- which were yes, yes, and yes -- would be handed directly to the lawyers of any case I would be assigned to later.

The rest of the hour was spent in an auditorium watching a film showing people dressed in Middle Ages period garb performing a trial by ordeal (tossing someone in the water to test their guilt -- float = guilty, drown = innocent), to show us how far we have come in these enlightened days, followed by a question and answer session by a septuagenarian judge whose cheerfulness and flamboyant mannerisms would have put Leo Buscaglia to shame. Oddly, the judge claimed that the process of trial by jury began with the Magna Carta, ignoring the Athenian's use of jurors some 1800 years earlier. Perhaps the 500 jurors of Socrates rings a bell, judge? No?

A more credible fact brought up in the lecture was that of the 400 people summoned for this week's service, less than 200 showed up, which is about average. I've come up with two explanations for this, neither of which bode well for my country. First, companies are not required to pay you while you're on jury duty, and the courts only pay you a nominal wage ($20/day) meant to cover parking and lunch. Second, people consider themselves consumers and not citizens, and have no sense of civic duty.

"But wait," you may be saying, "didn't you yourself try to get out of jury duty? Isn't it hypocritical to claim other people aren't civic-minded?" To answer, here is the text of the letter I sent to the jury commission:

Request for Curtis Autery being excused from jury duty for child care reasons

Dear sirs,

My wife, Liberty, has late classes at OSU on Tuesdays and Thursdays. These classes run until 5:18pm. On these days, I pick up my daughter, Scout, from school around 4pm so that she can have dinner and get started on her homework.

If I were to serve jury duty, Scout would be required to stay in after-school care on these days, which is only available until 6pm. The time it would take Liberty to get to her car and then fight rush-hour traffic to get to Scout’s school would typically have her arriving after 6pm. This would place a financial burden on us in paying fines each day this happened (which would be most Tuesdays and Thursdays), and the disruption of Scout’s well-being as she would have a late dinner and not get started on her homework until she was tired in the evening.

I respectfully request to be excused from this jury duty assignment. With that said, I welcome the opportunity to serve, and each semester at OSU brings my wife a different schedule, so this disruption may not apply should I get summoned again in the future.

Thank you very much.

Curtis Autery
[address, phone]

The letter mentions that I would like another chance to serve if they excused me this time, and when told to quit whining and show up like a man, that's exactly what I did.

The $20/day and employers not being required to pay is more interesting, though. If you have a working class job that doesn't pay for jury service, you're probably living paycheck to paycheck already, and can't afford the time off, and hence can't serve. Many criminal cases involve defendants with working class jobs. How then, can they get a jury of their peers?

Or let's take the racial angle: If you live in an area with rich white people and poor black people, and a black man is on trial, what are the jurors likely to be? White, because they can either afford the time off, or their employers pay their normal salary during jury service. Are they likely to be sympathetic to the black man on trial? No. Biased against? Yes.

I don't consider myself to be especially political or an activist, but the way jury service is run is a clear disservice to my fellow man, perhaps explaining why there are so many black men in prison, many of which are later found not to be guilty of their accused crimes through the help of The Innocence Project.

On with the story.

Day 1 continued with waiting for a trial to start, which happened roughly 30 minutes later, and I was one of the 24 people called up to be potential jurors. The case was Zimara Ball v. Jessica Stark, involving (from the pretrial statement) "an automobile/pedestrian accident which occurred on June 3, 2006, when then10-yearold Zimara Ball darted onto Brown Road ... As Zimara Ball did so, she ran into the passenger side front quarter panel of a vehicle being driven by Defendant Jessica Stark."

Per directions from the court, I refrained from looking up anything about the case until I was discharged from jury service. Oddly, and despite being a seasoned data miner, I can find no mention of this incident in the news when it happened, or coverage of the current trial. Jessica's employer at the time, Maronda homes, has painstakingly expunged any reference to her from its website. News site searches for both parties reveals nothing other than Zimara making the 8th grade honor roll this year -- congratulations! The only information I could find about the case was on the court website itself, which is kind enough to supply scanned copies of all the motions and filings.

The courtroom had a handful of people in it before I and my fellow potential jurors came in. The plaintiff's mom (effectively the real plaintiff) and her legal staff, Jessica and her legal staff, a lawyer representing Maronda Homes, the judge, the court reporter, and a couple random people with no apparent function to serve were all standing and waiting for us to come in and find our seats. After we were sworn in, the judge began to explain voir dire, the process of weeding out bad jurors.

This was a civil trial, meaning there are 8 jurors and two alternates, and only a 3/4 majority is needed to decide guilt. The judge, and then the lawyers, would use our questionnaires, and direct and indirect questioning to determine if anyone shouldn't be on the jury. The reasons one wouldn't be appropriate to be on the jury would be having a bias against "the system", personally knowing any of the parties, having passable knowledge of anything expert witnesses would testify about (I have mixed feelings about this one), or having a similar personal experience to what was being tried.

So around the room the judge went, and around the room the lawyers went, and in about an hour we found that two men had children that had been murdered, a mom had severe anxiety about child safety, a narcissistic woman habitually receives traffic tickets and distrusts any police testimony, I myself have been hit by a car while bicycling, and just about everyone had been in court for some reason before. The parents of the murdered children, crying-towel mom, and the spazzy driver were all let go, but for whatever reason they kept me on until the second day.

Here is where some distasteful things happen. Here is where lawyer jokes come from. In fact, here's one now: Q) How do you save a lawyer from drowning? A) Take your foot off his head.

The judge painstakingly explains why not discussing the case or drawing any conclusions early is important. One of the reasons he gives is the following example of two jurors, let's call them George and Bob, talking about the case over lunch...

"Gee, Bob, I really didn't find that last witness convincing. I think he's lying." George has just committed to a point of view out loud, and for some people it's difficult to go against an opinion you've stated openly. If George now hears more evidence that supports the witness he thought was lying, he will be more hesitant to change his mind than if he had said nothing. Apparently saying "I may have been wrong before" is difficult for people. Or possibly nobody reads Emerson₁ any more.

On top of the admonition not to talk about the case, it was made clear that we weren't trying the case, or hearing any evidence in it yet. We were instead in a vague, nebulous discussion about issues that may come up during the trial and whether our personal biases would put objectivity in peril before any real evidence was heard.

The judge was specifically avoiding giving out information about the case with his questions, and avoiding questions leading us to profess a belief. The lawyers, however, had no such qualms. Objections flew, and the judge stopped the questioning on his own multiple times, as the lawyers jockeyed for position.

The plaintiff's lawyer asked us all to commit, under oath, to the belief that everyone should always, under all circumstances, slow down when a child is anywhere near a road. This tells me two things: The defendant didn't slow down, and there is a reason that she didn't think she needed to. And the lawyer wanted me to say "oh yes, there can never be a reason not to instantaneously slow down when a kid is present." Having delivered pizza for two years, and being a father, I understand that kids have no peripheral vision, no understanding of physics or consequences, follow bouncing balls into the street like a moth to a flame, and can generally be assumed to be at least unpredictable, if not batshit crazy. None of that implies, though, that braking should be automatic whenever there are any kids anywhere. The question implied that there is some ambiguity about whether slowing was appropriate, and some of us already began to commit to a point of view we might want to reconsider later, exactly the type of thing the judge warned us not to do.

He next asked us if we had ever hit anything in our car that we didn't see, and all who answered in the affirmative were later excused from the case. So the defendant probably claims to have not seen the girl darting into the road, and later the plaintiff's lawyer will claim this not to be possible.

The defendant's lawyer had her turn then, and went on a rant about today's children looking older than they are, trying to get everyone to admit that they were bad judges of kids' ages, just like her client. And then the question of how old a kid should be before she should be considered competent to cross a street unassisted came up. We had already heard at this point that the accident happened when the girl was 10, a nice round number, and at least half of the remaining jurors put 10 as the age at which kids shouldn't be darting out into traffic any more. So the defendant may have seen the kid or may not, and if she did, then she thought the kid was older, but either way, believes that once you're 10 you shouldn't be doing anything stupid like that anyway. So there are lots of possible defenses in play, and the lawyer was getting a read on which one would work best.

So that pretty much laid the whole trial out, right there in the voir dire proceeding, with at least two thirds of us committing to some solid point of view that the lawyers will be trying to leverage throughout the trial. This was all the exact opposite of what was supposed to be happening, and all the court officials played this theater of pretending nothing mistrial-worthy had just happened.

I was sickened, and once the day's proceedings were over, was very glad to go home.

Day 2 involved a lot of waiting, and none of the preceding day's ethical problems. I parked my car at my work's garage, hoofed it to the courthouse, put on my juror's badge to make me an un-person -- to warn off lawyers and case parties from engaging in conversation with me (strangers don't tend to seek out my conversation, so I wasn't very concerned about this) -- signed in at the jury pool waiting room, and headed up to the sixth floor where our courtroom was. We assembled at 9:30, entered the courtroom, and were asked a single question from the judge: "Did you hear the news story last night about the traffic accident?" We were then told to leave and re-assemble at 10. At 10:15, they finally called us back in, where they announced that the jury had been selected. Ten of our names were read. My name wasn't one of them.

I spent the rest of my time in the insanely hot jury pool waiting room, reading "The Terror" by Dan Simmons. By day 3 I had finished the first 100 pages, and couldn't sit in the uncomfortable chairs any longer, so got up and meandered over to find the newspaper editorials, yellowed with age, espousing the awesomeness of jury duty, being a citizen, and America itself. I like America just fine, and the benefits of being a citizen, and I don't shirk the duties that come with that, but the duties aren't as rose-colored as puff-piece articles would lead one to believe.

1 - From Ralph Waldo Emerson's "Self-Reliance": Speak what you think now in hard words, and to-morrow speak what to-morrow thinks in hard words again, though it contradict every thing you said to-day.

Awesome Ted talks

2010-10-24T20:55:00.001-04:00

(plus some David Byrne worship, because he rocks)
(and Seth Godin at GEL, who also rocks)

David Byrne sings Nothing but Flowers

How architecture helped music evolve

How schools kill creativity

Malcolm Gladwell on spaghetti sauce

The child-driven education. If you only pick one to watch, pick this one.

Economic reality check

The good news of the decade. Wait out the odd opening for a kickin' conclusion.

This is broken!

Fun music videos, mostly 80s

2010-10-23T10:20:00.004-04:00

Some videos that are cool. No reason.

JavaScript Roman numeral calculator

2010-10-09T06:34:00.011-04:00

Yesterday I saw a homework question on a coding forum I frequent regarding turning Arabic numbers into Roman numerals. Homework questions are a strange breed. Most of the time the posters are blatantly cheating, some times they are up front that the question is for an assignment and they just want a push in the right direction. Responses range from helpful, following the Wikipedia "assume good faith" mantra, to cynical, to pretty damned rude. Forum admins enjoy flexing their dictatorial muscles in these cases, posting warnings, flames, and deleting posts.

My mantra in these cases is simple: If the question is interesting, I try to answer it. If the poster isn't cut out for a programming career, getting my answer isn't going to change that. If he is, he's going to be asking his peers a lot of questions over his career, as no one is born with an innate gift at coding; it's a learned skill like anything else. The young "super hacker" is generally the geek equivalent of a bully - not as skilled/tough as he pretends.

I'm using "he" and "his" a lot here, which is deliberate. There are women coders, sure, but for whatever reason they don't frequent the programming forums. I can only assume they tackle problems more intelligently, like asking a trusted source they know personally, or using things like Google.

End sidebar.

Anyway, I was as familiar as most people with how Roman numerals worked, namely numbers less than 40 made sense, then they get strange with the Ls, Cs, Ds, and Ms. So, I did a little research to fill in my knowledge gap. As it turns out, the concept is pretty straightforward, and revolves around powers of 10. For each power of 10, there are 4 cases: 1-3, 4, 5-8, and 9. Observe:

  1 = I     4 = IV   5 = V      9 = IX
  2 = II             6 = VI  
  3 = III            7 = VII 
                     8 = VIII
           
 10 = X    40 = XL  50 = L     90 = XC
 20 = XX            60 = LX  
 30 = XXX           70 = LXX 
                    80 = LXXX
          
100 = C   400 = CD 500 = D    900 = CM         
200 = CC           600 = DC  
300 = CCC          700 = DCC 
                   800 = DCCC

Not so daunting, after all. These can be pieced together to build any number under 1000. For numbers between 1000 and 3999, just prepend with one M for every thousand. After that it gets weird with overscores, where a line over a letter means its value is multiplied by 1000. There seems to be little support for fonts with overscores, so I stuck with numbers under 4000.

I tackled conversion without using any fancy coding constructs, instead just walking an input number down to 0 while building up the Roman numeral string:

var s = "";
while (num >= 1000) { num -= 1000; s +=  "M"; }
if    (num >=  900) { num -=  900; s += "CM"; }
if    (num >=  500) { num -=  500; s +=  "D"; }
if    (num >=  400) { num -=  400; s += "CD"; }
while (num >=  100) { num -=  100; s +=  "C"; }
if    (num >=   90) { num -=   90; s += "XC"; }
if    (num >=   50) { num -=   50; s +=  "L"; }
if    (num >=   40) { num -=   40; s += "XL"; }
while (num >=   10) { num -=   10; s +=  "X"; }
if    (num >=    9) { num -=    9; s += "IX"; }
if    (num >=    5) { num -=    5; s +=  "V"; }
if    (num >=    4) { num -=    4; s += "IV"; }
while (num >=    1) { num -=    1; s +=  "I"; }
return s;

Try it out:

Enter a number between 1 and 3999:
Roman numeral:

Also, there aren't any good lists of Roman numeral sequences on the Internet. They either stop at 100 and explain continuation rules, or are space-delimited with no associated Arabic numbers, or use the HTML "ordered list" trick, where you can bullet-point list items with Roman numerals that, sadly, can't be copied to your clipboard.

To correct that oversight, here is a simple, copyable, well-formatted list of Roman numerals between 1 and 3999:

   1 = I
   2 = II
   3 = III
   4 = IV
   5 = V
   6 = VI
   7 = VII
   8 = VIII
   9 = IX
  10 = X
  11 = XI
  12 = XII
  13 = XIII
  14 = XIV
  15 = XV
  16 = XVI
  17 = XVII
  18 = XVIII
  19 = XIX
  20 = XX
  21 = XXI
  22 = XXII
  23 = XXIII
  24 = XXIV
  25 = XXV
  26 = XXVI
  27 = XXVII
  28 = XXVIII
  29 = XXIX
  30 = XXX
  31 = XXXI
  32 = XXXII
  33 = XXXIII
  34 = XXXIV
  35 = XXXV
  36 = XXXVI
  37 = XXXVII
  38 = XXXVIII
  39 = XXXIX
  40 = XL
  41 = XLI
  42 = XLII
  43 = XLIII
  44 = XLIV
  45 = XLV
  46 = XLVI
  47 = XLVII
  48 = XLVIII
  49 = XLIX
  50 = L
  51 = LI
  52 = LII
  53 = LIII
  54 = LIV
  55 = LV
  56 = LVI
  57 = LVII
  58 = LVIII
  59 = LIX
  60 = LX
  61 = LXI
  62 = LXII
  63 = LXIII
  64 = LXIV
  65 = LXV
  66 = LXVI
  67 = LXVII
  68 = LXVIII
  69 = LXIX
  70 = LXX
  71 = LXXI
  72 = LXXII
  73 = LXXIII
  74 = LXXIV
  75 = LXXV
  76 = LXXVI
  77 = LXXVII
  78 = LXXVIII
  79 = LXXIX
  80 = LXXX
  81 = LXXXI
  82 = LXXXII
  83 = LXXXIII
  84 = LXXXIV
  85 = LXXXV
  86 = LXXXVI
  87 = LXXXVII
  88 = LXXXVIII
  89 = LXXXIX
  90 = XC
  91 = XCI
  92 = XCII
  93 = XCIII
  94 = XCIV
  95 = XCV
  96 = XCVI
  97 = XCVII
  98 = XCVIII
  99 = XCIX
 100 = C
 101 = CI
 102 = CII
 103 = CIII
 104 = CIV
 105 = CV
 106 = CVI
 107 = CVII
 108 = CVIII
 109 = CIX
 110 = CX
 111 = CXI
 112 = CXII
 113 = CXIII
 114 = CXIV
 115 = CXV
 116 = CXVI
 117 = CXVII
 118 = CXVIII
 119 = CXIX
 120 = CXX
 121 = CXXI
 122 = CXXII
 123 = CXXIII
 124 = CXXIV
 125 = CXXV
 126 = CXXVI
 127 = CXXVII
 128 = CXXVIII
 129 = CXXIX
 130 = CXXX
 131 = CXXXI
 132 = CXXXII
 133 = CXXXIII
 134 = CXXXIV
 135 = CXXXV
 136 = CXXXVI
 137 = CXXXVII
 138 = CXXXVIII
 139 = CXXXIX
 140 = CXL
 141 = CXLI
 142 = CXLII
 143 = CXLIII
 144 = CXLIV
 145 = CXLV
 146 = CXLVI
 147 = CXLVII
 148 = CXLVIII
 149 = CXLIX
 150 = CL
 151 = CLI
 152 = CLII
 153 = CLIII
 154 = CLIV
 155 = CLV
 156 = CLVI
 157 = CLVII
 158 = CLVIII
 159 = CLIX
 160 = CLX
 161 = CLXI
 162 = CLXII
 163 = CLXIII
 164 = CLXIV
 165 = CLXV
 166 = CLXVI
 167 = CLXVII
 168 = CLXVIII
 169 = CLXIX
 170 = CLXX
 171 = CLXXI
 172 = CLXXII
 173 = CLXXIII
 174 = CLXXIV
 175 = CLXXV
 176 = CLXXVI
 177 = CLXXVII
 178 = CLXXVIII
 179 = CLXXIX
 180 = CLXXX
 181 = CLXXXI
 182 = CLXXXII
 183 = CLXXXIII
 184 = CLXXXIV
 185 = CLXXXV
 186 = CLXXXVI
 187 = CLXXXVII
 188 = CLXXXVIII
 189 = CLXXXIX
 190 = CXC
 191 = CXCI
 192 = CXCII
 193 = CXCIII
 194 = CXCIV
 195 = CXCV
 196 = CXCVI
 197 = CXCVII
 198 = CXCVIII
 199 = CXCIX
 200 = CC
 201 = CCI
 202 = CCII
 203 = CCIII
 204 = CCIV
 205 = CCV
 206 = CCVI
 207 = CCVII
 208 = CCVIII
 209 = CCIX
 210 = CCX
 211 = CCXI
 212 = CCXII
 213 = CCXIII
 214 = CCXIV
 215 = CCXV
 216 = CCXVI
 217 = CCXVII
 218 = CCXVIII
 219 = CCXIX
 220 = CCXX
 221 = CCXXI
 222 = CCXXII
 223 = CCXXIII
 224 = CCXXIV
 225 = CCXXV
 226 = CCXXVI
 227 = CCXXVII
 228 = CCXXVIII
 229 = CCXXIX
 230 = CCXXX
 231 = CCXXXI
 232 = CCXXXII
 233 = CCXXXIII
 234 = CCXXXIV
 235 = CCXXXV
 236 = CCXXXVI
 237 = CCXXXVII
 238 = CCXXXVIII
 239 = CCXXXIX
 240 = CCXL
 241 = CCXLI
 242 = CCXLII
 243 = CCXLIII
 244 = CCXLIV
 245 = CCXLV
 246 = CCXLVI
 247 = CCXLVII
 248 = CCXLVIII
 249 = CCXLIX
 250 = CCL
 251 = CCLI
 252 = CCLII
 253 = CCLIII
 254 = CCLIV
 255 = CCLV
 256 = CCLVI
 257 = CCLVII
 258 = CCLVIII
 259 = CCLIX
 260 = CCLX
 261 = CCLXI
 262 = CCLXII
 263 = CCLXIII
 264 = CCLXIV
 265 = CCLXV
 266 = CCLXVI
 267 = CCLXVII
 268 = CCLXVIII
 269 = CCLXIX
 270 = CCLXX
 271 = CCLXXI
 272 = CCLXXII
 273 = CCLXXIII
 274 = CCLXXIV
 275 = CCLXXV
 276 = CCLXXVI
 277 = CCLXXVII
 278 = CCLXXVIII
 279 = CCLXXIX
 280 = CCLXXX
 281 = CCLXXXI
 282 = CCLXXXII
 283 = CCLXXXIII
 284 = CCLXXXIV
 285 = CCLXXXV
 286 = CCLXXXVI
 287 = CCLXXXVII
 288 = CCLXXXVIII
 289 = CCLXXXIX
 290 = CCXC
 291 = CCXCI
 292 = CCXCII
 293 = CCXCIII
 294 = CCXCIV
 295 = CCXCV
 296 = CCXCVI
 297 = CCXCVII
 298 = CCXCVIII
 299 = CCXCIX
 300 = CCC
 301 = CCCI
 302 = CCCII
 303 = CCCIII
 304 = CCCIV
 305 = CCCV
 306 = CCCVI
 307 = CCCVII
 308 = CCCVIII
 309 = CCCIX
 310 = CCCX
 311 = CCCXI
 312 = CCCXII
 313 = CCCXIII
 314 = CCCXIV
 315 = CCCXV
 316 = CCCXVI
 317 = CCCXVII
 318 = CCCXVIII
 319 = CCCXIX
 320 = CCCXX
 321 = CCCXXI
 322 = CCCXXII
 323 = CCCXXIII
 324 = CCCXXIV
 325 = CCCXXV
 326 = CCCXXVI
 327 = CCCXXVII
 328 = CCCXXVIII
 329 = CCCXXIX
 330 = CCCXXX
 331 = CCCXXXI
 332 = CCCXXXII
 333 = CCCXXXIII
 334 = CCCXXXIV
 335 = CCCXXXV
 336 = CCCXXXVI
 337 = CCCXXXVII
 338 = CCCXXXVIII
 339 = CCCXXXIX
 340 = CCCXL
 341 = CCCXLI
 342 = CCCXLII
 343 = CCCXLIII
 344 = CCCXLIV
 345 = CCCXLV
 346 = CCCXLVI
 347 = CCCXLVII
 348 = CCCXLVIII
 349 = CCCXLIX
 350 = CCCL
 351 = CCCLI
 352 = CCCLII
 353 = CCCLIII
 354 = CCCLIV
 355 = CCCLV
 356 = CCCLVI
 357 = CCCLVII
 358 = CCCLVIII
 359 = CCCLIX
 360 = CCCLX
 361 = CCCLXI
 362 = CCCLXII
 363 = CCCLXIII
 364 = CCCLXIV
 365 = CCCLXV
 366 = CCCLXVI
 367 = CCCLXVII
 368 = CCCLXVIII
 369 = CCCLXIX
 370 = CCCLXX
 371 = CCCLXXI
 372 = CCCLXXII
 373 = CCCLXXIII
 374 = CCCLXXIV
 375 = CCCLXXV
 376 = CCCLXXVI
 377 = CCCLXXVII
 378 = CCCLXXVIII
 379 = CCCLXXIX
 380 = CCCLXXX
 381 = CCCLXXXI
 382 = CCCLXXXII
 383 = CCCLXXXIII
 384 = CCCLXXXIV
 385 = CCCLXXXV
 386 = CCCLXXXVI
 387 = CCCLXXXVII
 388 = CCCLXXXVIII
 389 = CCCLXXXIX
 390 = CCCXC
 391 = CCCXCI
 392 = CCCXCII
 393 = CCCXCIII
 394 = CCCXCIV
 395 = CCCXCV
 396 = CCCXCVI
 397 = CCCXCVII
 398 = CCCXCVIII
 399 = CCCXCIX
 400 = CD
 401 = CDI
 402 = CDII
 403 = CDIII
 404 = CDIV
 405 = CDV
 406 = CDVI
 407 = CDVII
 408 = CDVIII
 409 = CDIX
 410 = CDX
 411 = CDXI
 412 = CDXII
 413 = CDXIII
 414 = CDXIV
 415 = CDXV
 416 = CDXVI
 417 = CDXVII
 418 = CDXVIII
 419 = CDXIX
 420 = CDXX
 421 = CDXXI
 422 = CDXXII
 423 = CDXXIII
 424 = CDXXIV
 425 = CDXXV
 426 = CDXXVI
 427 = CDXXVII
 428 = CDXXVIII
 429 = CDXXIX
 430 = CDXXX
 431 = CDXXXI
 432 = CDXXXII
 433 = CDXXXIII
 434 = CDXXXIV
 435 = CDXXXV
 436 = CDXXXVI
 437 = CDXXXVII
 438 = CDXXXVIII
 439 = CDXXXIX
 440 = CDXL
 441 = CDXLI
 442 = CDXLII
 443 = CDXLIII
 444 = CDXLIV
 445 = CDXLV
 446 = CDXLVI
 447 = CDXLVII
 448 = CDXLVIII
 449 = CDXLIX
 450 = CDL
 451 = CDLI
 452 = CDLII
 453 = CDLIII
 454 = CDLIV
 455 = CDLV
 456 = CDLVI
 457 = CDLVII
 458 = CDLVIII
 459 = CDLIX
 460 = CDLX
 461 = CDLXI
 462 = CDLXII
 463 = CDLXIII
 464 = CDLXIV
 465 = CDLXV
 466 = CDLXVI
 467 = CDLXVII
 468 = CDLXVIII
 469 = CDLXIX
 470 = CDLXX
 471 = CDLXXI
 472 = CDLXXII
 473 = CDLXXIII
 474 = CDLXXIV
 475 = CDLXXV
 476 = CDLXXVI
 477 = CDLXXVII
 478 = CDLXXVIII
 479 = CDLXXIX
 480 = CDLXXX
 481 = CDLXXXI
 482 = CDLXXXII
 483 = CDLXXXIII
 484 = CDLXXXIV
 485 = CDLXXXV
 486 = CDLXXXVI
 487 = CDLXXXVII
 488 = CDLXXXVIII
 489 = CDLXXXIX
 490 = CDXC
 491 = CDXCI
 492 = CDXCII
 493 = CDXCIII
 494 = CDXCIV
 495 = CDXCV
 496 = CDXCVI
 497 = CDXCVII
 498 = CDXCVIII
 499 = CDXCIX
 500 = D
 501 = DI
 502 = DII
 503 = DIII
 504 = DIV
 505 = DV
 506 = DVI
 507 = DVII
 508 = DVIII
 509 = DIX
 510 = DX
 511 = DXI
 512 = DXII
 513 = DXIII
 514 = DXIV
 515 = DXV
 516 = DXVI
 517 = DXVII
 518 = DXVIII
 519 = DXIX
 520 = DXX
 521 = DXXI
 522 = DXXII
 523 = DXXIII
 524 = DXXIV
 525 = DXXV
 526 = DXXVI
 527 = DXXVII
 528 = DXXVIII
 529 = DXXIX
 530 = DXXX
 531 = DXXXI
 532 = DXXXII
 533 = DXXXIII
 534 = DXXXIV
 535 = DXXXV
 536 = DXXXVI
 537 = DXXXVII
 538 = DXXXVIII
 539 = DXXXIX
 540 = DXL
 541 = DXLI
 542 = DXLII
 543 = DXLIII
 544 = DXLIV
 545 = DXLV
 546 = DXLVI
 547 = DXLVII
 548 = DXLVIII
 549 = DXLIX
 550 = DL
 551 = DLI
 552 = DLII
 553 = DLIII
 554 = DLIV
 555 = DLV
 556 = DLVI
 557 = DLVII
 558 = DLVIII
 559 = DLIX
 560 = DLX
 561 = DLXI
 562 = DLXII
 563 = DLXIII
 564 = DLXIV
 565 = DLXV
 566 = DLXVI
 567 = DLXVII
 568 = DLXVIII
 569 = DLXIX
 570 = DLXX
 571 = DLXXI
 572 = DLXXII
 573 = DLXXIII
 574 = DLXXIV
 575 = DLXXV
 576 = DLXXVI
 577 = DLXXVII
 578 = DLXXVIII
 579 = DLXXIX
 580 = DLXXX
 581 = DLXXXI
 582 = DLXXXII
 583 = DLXXXIII
 584 = DLXXXIV
 585 = DLXXXV
 586 = DLXXXVI
 587 = DLXXXVII
 588 = DLXXXVIII
 589 = DLXXXIX
 590 = DXC
 591 = DXCI
 592 = DXCII
 593 = DXCIII
 594 = DXCIV
 595 = DXCV
 596 = DXCVI
 597 = DXCVII
 598 = DXCVIII
 599 = DXCIX
 600 = DC
 601 = DCI
 602 = DCII
 603 = DCIII
 604 = DCIV
 605 = DCV
 606 = DCVI
 607 = DCVII
 608 = DCVIII
 609 = DCIX
 610 = DCX
 611 = DCXI
 612 = DCXII
 613 = DCXIII
 614 = DCXIV
 615 = DCXV
 616 = DCXVI
 617 = DCXVII
 618 = DCXVIII
 619 = DCXIX
 620 = DCXX
 621 = DCXXI
 622 = DCXXII
 623 = DCXXIII
 624 = DCXXIV
 625 = DCXXV
 626 = DCXXVI
 627 = DCXXVII
 628 = DCXXVIII
 629 = DCXXIX
 630 = DCXXX
 631 = DCXXXI
 632 = DCXXXII
 633 = DCXXXIII
 634 = DCXXXIV
 635 = DCXXXV
 636 = DCXXXVI
 637 = DCXXXVII
 638 = DCXXXVIII
 639 = DCXXXIX
 640 = DCXL
 641 = DCXLI
 642 = DCXLII
 643 = DCXLIII
 644 = DCXLIV
 645 = DCXLV
 646 = DCXLVI
 647 = DCXLVII
 648 = DCXLVIII
 649 = DCXLIX
 650 = DCL
 651 = DCLI
 652 = DCLII
 653 = DCLIII
 654 = DCLIV
 655 = DCLV
 656 = DCLVI
 657 = DCLVII
 658 = DCLVIII
 659 = DCLIX
 660 = DCLX
 661 = DCLXI
 662 = DCLXII
 663 = DCLXIII
 664 = DCLXIV
 665 = DCLXV
 666 = DCLXVI
 667 = DCLXVII
 668 = DCLXVIII
 669 = DCLXIX
 670 = DCLXX
 671 = DCLXXI
 672 = DCLXXII
 673 = DCLXXIII
 674 = DCLXXIV
 675 = DCLXXV
 676 = DCLXXVI
 677 = DCLXXVII
 678 = DCLXXVIII
 679 = DCLXXIX
 680 = DCLXXX
 681 = DCLXXXI
 682 = DCLXXXII
 683 = DCLXXXIII
 684 = DCLXXXIV
 685 = DCLXXXV
 686 = DCLXXXVI
 687 = DCLXXXVII
 688 = DCLXXXVIII
 689 = DCLXXXIX
 690 = DCXC
 691 = DCXCI
 692 = DCXCII
 693 = DCXCIII
 694 = DCXCIV
 695 = DCXCV
 696 = DCXCVI
 697 = DCXCVII
 698 = DCXCVIII
 699 = DCXCIX
 700 = DCC
 701 = DCCI
 702 = DCCII
 703 = DCCIII
 704 = DCCIV
 705 = DCCV
 706 = DCCVI
 707 = DCCVII
 708 = DCCVIII
 709 = DCCIX
 710 = DCCX
 711 = DCCXI
 712 = DCCXII
 713 = DCCXIII
 714 = DCCXIV
 715 = DCCXV
 716 = DCCXVI
 717 = DCCXVII
 718 = DCCXVIII
 719 = DCCXIX
 720 = DCCXX
 721 = DCCXXI
 722 = DCCXXII
 723 = DCCXXIII
 724 = DCCXXIV
 725 = DCCXXV
 726 = DCCXXVI
 727 = DCCXXVII
 728 = DCCXXVIII
 729 = DCCXXIX
 730 = DCCXXX
 731 = DCCXXXI
 732 = DCCXXXII
 733 = DCCXXXIII
 734 = DCCXXXIV
 735 = DCCXXXV
 736 = DCCXXXVI
 737 = DCCXXXVII
 738 = DCCXXXVIII
 739 = DCCXXXIX
 740 = DCCXL
 741 = DCCXLI
 742 = DCCXLII
 743 = DCCXLIII
 744 = DCCXLIV
 745 = DCCXLV
 746 = DCCXLVI
 747 = DCCXLVII
 748 = DCCXLVIII
 749 = DCCXLIX
 750 = DCCL
 751 = DCCLI
 752 = DCCLII
 753 = DCCLIII
 754 = DCCLIV
 755 = DCCLV
 756 = DCCLVI
 757 = DCCLVII
 758 = DCCLVIII
 759 = DCCLIX
 760 = DCCLX
 761 = DCCLXI
 762 = DCCLXII
 763 = DCCLXIII
 764 = DCCLXIV
 765 = DCCLXV
 766 = DCCLXVI
 767 = DCCLXVII
 768 = DCCLXVIII
 769 = DCCLXIX
 770 = DCCLXX
 771 = DCCLXXI
 772 = DCCLXXII
 773 = DCCLXXIII
 774 = DCCLXXIV
 775 = DCCLXXV
 776 = DCCLXXVI
 777 = DCCLXXVII
 778 = DCCLXXVIII
 779 = DCCLXXIX
 780 = DCCLXXX
 781 = DCCLXXXI
 782 = DCCLXXXII
 783 = DCCLXXXIII
 784 = DCCLXXXIV
 785 = DCCLXXXV
 786 = DCCLXXXVI
 787 = DCCLXXXVII
 788 = DCCLXXXVIII
 789 = DCCLXXXIX
 790 = DCCXC
 791 = DCCXCI
 792 = DCCXCII
 793 = DCCXCIII
 794 = DCCXCIV
 795 = DCCXCV
 796 = DCCXCVI
 797 = DCCXCVII
 798 = DCCXCVIII
 799 = DCCXCIX
 800 = DCCC
 801 = DCCCI
 802 = DCCCII
 803 = DCCCIII
 804 = DCCCIV
 805 = DCCCV
 806 = DCCCVI
 807 = DCCCVII
 808 = DCCCVIII
 809 = DCCCIX
 810 = DCCCX
 811 = DCCCXI
 812 = DCCCXII
 813 = DCCCXIII
 814 = DCCCXIV
 815 = DCCCXV
 816 = DCCCXVI
 817 = DCCCXVII
 818 = DCCCXVIII
 819 = DCCCXIX
 820 = DCCCXX
 821 = DCCCXXI
 822 = DCCCXXII
 823 = DCCCXXIII
 824 = DCCCXXIV
 825 = DCCCXXV
 826 = DCCCXXVI
 827 = DCCCXXVII
 828 = DCCCXXVIII
 829 = DCCCXXIX
 830 = DCCCXXX
 831 = DCCCXXXI
 832 = DCCCXXXII
 833 = DCCCXXXIII
 834 = DCCCXXXIV
 835 = DCCCXXXV
 836 = DCCCXXXVI
 837 = DCCCXXXVII
 838 = DCCCXXXVIII
 839 = DCCCXXXIX
 840 = DCCCXL
 841 = DCCCXLI
 842 = DCCCXLII
 843 = DCCCXLIII
 844 = DCCCXLIV
 845 = DCCCXLV
 846 = DCCCXLVI
 847 = DCCCXLVII
 848 = DCCCXLVIII
 849 = DCCCXLIX
 850 = DCCCL
 851 = DCCCLI
 852 = DCCCLII
 853 = DCCCLIII
 854 = DCCCLIV
 855 = DCCCLV
 856 = DCCCLVI
 857 = DCCCLVII
 858 = DCCCLVIII
 859 = DCCCLIX
 860 = DCCCLX
 861 = DCCCLXI
 862 = DCCCLXII
 863 = DCCCLXIII
 864 = DCCCLXIV
 865 = DCCCLXV
 866 = DCCCLXVI
 867 = DCCCLXVII
 868 = DCCCLXVIII
 869 = DCCCLXIX
 870 = DCCCLXX
 871 = DCCCLXXI
 872 = DCCCLXXII
 873 = DCCCLXXIII
 874 = DCCCLXXIV
 875 = DCCCLXXV
 876 = DCCCLXXVI
 877 = DCCCLXXVII
 878 = DCCCLXXVIII
 879 = DCCCLXXIX
 880 = DCCCLXXX
 881 = DCCCLXXXI
 882 = DCCCLXXXII
 883 = DCCCLXXXIII
 884 = DCCCLXXXIV
 885 = DCCCLXXXV
 886 = DCCCLXXXVI
 887 = DCCCLXXXVII
 888 = DCCCLXXXVIII
 889 = DCCCLXXXIX
 890 = DCCCXC
 891 = DCCCXCI
 892 = DCCCXCII
 893 = DCCCXCIII
 894 = DCCCXCIV
 895 = DCCCXCV
 896 = DCCCXCVI
 897 = DCCCXCVII
 898 = DCCCXCVIII
 899 = DCCCXCIX
 900 = CM
 901 = CMI
 902 = CMII
 903 = CMIII
 904 = CMIV
 905 = CMV
 906 = CMVI
 907 = CMVII
 908 = CMVIII
 909 = CMIX
 910 = CMX
 911 = CMXI
 912 = CMXII
 913 = CMXIII
 914 = CMXIV
 915 = CMXV
 916 = CMXVI
 917 = CMXVII
 918 = CMXVIII
 919 = CMXIX
 920 = CMXX
 921 = CMXXI
 922 = CMXXII
 923 = CMXXIII
 924 = CMXXIV
 925 = CMXXV
 926 = CMXXVI
 927 = CMXXVII
 928 = CMXXVIII
 929 = CMXXIX
 930 = CMXXX
 931 = CMXXXI
 932 = CMXXXII
 933 = CMXXXIII
 934 = CMXXXIV
 935 = CMXXXV
 936 = CMXXXVI
 937 = CMXXXVII
 938 = CMXXXVIII
 939 = CMXXXIX
 940 = CMXL
 941 = CMXLI
 942 = CMXLII
 943 = CMXLIII
 944 = CMXLIV
 945 = CMXLV
 946 = CMXLVI
 947 = CMXLVII
 948 = CMXLVIII
 949 = CMXLIX
 950 = CML
 951 = CMLI
 952 = CMLII
 953 = CMLIII
 954 = CMLIV
 955 = CMLV
 956 = CMLVI
 957 = CMLVII
 958 = CMLVIII
 959 = CMLIX
 960 = CMLX
 961 = CMLXI
 962 = CMLXII
 963 = CMLXIII
 964 = CMLXIV
 965 = CMLXV
 966 = CMLXVI
 967 = CMLXVII
 968 = CMLXVIII
 969 = CMLXIX
 970 = CMLXX
 971 = CMLXXI
 972 = CMLXXII
 973 = CMLXXIII
 974 = CMLXXIV
 975 = CMLXXV
 976 = CMLXXVI
 977 = CMLXXVII
 978 = CMLXXVIII
 979 = CMLXXIX
 980 = CMLXXX
 981 = CMLXXXI
 982 = CMLXXXII
 983 = CMLXXXIII
 984 = CMLXXXIV
 985 = CMLXXXV
 986 = CMLXXXVI
 987 = CMLXXXVII
 988 = CMLXXXVIII
 989 = CMLXXXIX
 990 = CMXC
 991 = CMXCI
 992 = CMXCII
 993 = CMXCIII
 994 = CMXCIV
 995 = CMXCV
 996 = CMXCVI
 997 = CMXCVII
 998 = CMXCVIII
 999 = CMXCIX
1000 = M
1001 = MI
1002 = MII
1003 = MIII
1004 = MIV
1005 = MV
1006 = MVI
1007 = MVII
1008 = MVIII
1009 = MIX
1010 = MX
1011 = MXI
1012 = MXII
1013 = MXIII
1014 = MXIV
1015 = MXV
1016 = MXVI
1017 = MXVII
1018 = MXVIII
1019 = MXIX
1020 = MXX
1021 = MXXI
1022 = MXXII
1023 = MXXIII
1024 = MXXIV
1025 = MXXV
1026 = MXXVI
1027 = MXXVII
1028 = MXXVIII
1029 = MXXIX
1030 = MXXX
1031 = MXXXI
1032 = MXXXII
1033 = MXXXIII
1034 = MXXXIV
1035 = MXXXV
1036 = MXXXVI
1037 = MXXXVII
1038 = MXXXVIII
1039 = MXXXIX
1040 = MXL
1041 = MXLI
1042 = MXLII
1043 = MXLIII
1044 = MXLIV
1045 = MXLV
1046 = MXLVI
1047 = MXLVII
1048 = MXLVIII
1049 = MXLIX
1050 = ML
1051 = MLI
1052 = MLII
1053 = MLIII
1054 = MLIV
1055 = MLV
1056 = MLVI
1057 = MLVII
1058 = MLVIII
1059 = MLIX
1060 = MLX
1061 = MLXI
1062 = MLXII
1063 = MLXIII
1064 = MLXIV
1065 = MLXV
1066 = MLXVI
1067 = MLXVII
1068 = MLXVIII
1069 = MLXIX
1070 = MLXX
1071 = MLXXI
1072 = MLXXII
1073 = MLXXIII
1074 = MLXXIV
1075 = MLXXV
1076 = MLXXVI
1077 = MLXXVII
1078 = MLXXVIII
1079 = MLXXIX
1080 = MLXXX
1081 = MLXXXI
1082 = MLXXXII
1083 = MLXXXIII
1084 = MLXXXIV
1085 = MLXXXV
1086 = MLXXXVI
1087 = MLXXXVII
1088 = MLXXXVIII
1089 = MLXXXIX
1090 = MXC
1091 = MXCI
1092 = MXCII
1093 = MXCIII
1094 = MXCIV
1095 = MXCV
1096 = MXCVI
1097 = MXCVII
1098 = MXCVIII
1099 = MXCIX
1100 = MC
1101 = MCI
1102 = MCII
1103 = MCIII
1104 = MCIV
1105 = MCV
1106 = MCVI
1107 = MCVII
1108 = MCVIII
1109 = MCIX
1110 = MCX
1111 = MCXI
1112 = MCXII
1113 = MCXIII
1114 = MCXIV
1115 = MCXV
1116 = MCXVI
1117 = MCXVII
1118 = MCXVIII
1119 = MCXIX
1120 = MCXX
1121 = MCXXI
1122 = MCXXII
1123 = MCXXIII
1124 = MCXXIV
1125 = MCXXV
1126 = MCXXVI
1127 = MCXXVII
1128 = MCXXVIII
1129 = MCXXIX
1130 = MCXXX
1131 = MCXXXI
1132 = MCXXXII
1133 = MCXXXIII
1134 = MCXXXIV
1135 = MCXXXV
1136 = MCXXXVI
1137 = MCXXXVII
1138 = MCXXXVIII
1139 = MCXXXIX
1140 = MCXL
1141 = MCXLI
1142 = MCXLII
1143 = MCXLIII
1144 = MCXLIV
1145 = MCXLV
1146 = MCXLVI
1147 = MCXLVII
1148 = MCXLVIII
1149 = MCXLIX
1150 = MCL
1151 = MCLI
1152 = MCLII
1153 = MCLIII
1154 = MCLIV
1155 = MCLV
1156 = MCLVI
1157 = MCLVII
1158 = MCLVIII
1159 = MCLIX
1160 = MCLX
1161 = MCLXI
1162 = MCLXII
1163 = MCLXIII
1164 = MCLXIV
1165 = MCLXV
1166 = MCLXVI
1167 = MCLXVII
1168 = MCLXVIII
1169 = MCLXIX
1170 = MCLXX
1171 = MCLXXI
1172 = MCLXXII
1173 = MCLXXIII
1174 = MCLXXIV
1175 = MCLXXV
1176 = MCLXXVI
1177 = MCLXXVII
1178 = MCLXXVIII
1179 = MCLXXIX
1180 = MCLXXX
1181 = MCLXXXI
1182 = MCLXXXII
1183 = MCLXXXIII
1184 = MCLXXXIV
1185 = MCLXXXV
1186 = MCLXXXVI
1187 = MCLXXXVII
1188 = MCLXXXVIII
1189 = MCLXXXIX
1190 = MCXC
1191 = MCXCI
1192 = MCXCII
1193 = MCXCIII
1194 = MCXCIV
1195 = MCXCV
1196 = MCXCVI
1197 = MCXCVII
1198 = MCXCVIII
1199 = MCXCIX
1200 = MCC
1201 = MCCI
1202 = MCCII
1203 = MCCIII
1204 = MCCIV
1205 = MCCV
1206 = MCCVI
1207 = MCCVII
1208 = MCCVIII
1209 = MCCIX
1210 = MCCX
1211 = MCCXI
1212 = MCCXII
1213 = MCCXIII
1214 = MCCXIV
1215 = MCCXV
1216 = MCCXVI
1217 = MCCXVII
1218 = MCCXVIII
1219 = MCCXIX
1220 = MCCXX
1221 = MCCXXI
1222 = MCCXXII
1223 = MCCXXIII
1224 = MCCXXIV
1225 = MCCXXV
1226 = MCCXXVI
1227 = MCCXXVII
1228 = MCCXXVIII
1229 = MCCXXIX
1230 = MCCXXX
1231 = MCCXXXI
1232 = MCCXXXII
1233 = MCCXXXIII
1234 = MCCXXXIV
1235 = MCCXXXV
1236 = MCCXXXVI
1237 = MCCXXXVII
1238 = MCCXXXVIII
1239 = MCCXXXIX
1240 = MCCXL
1241 = MCCXLI
1242 = MCCXLII
1243 = MCCXLIII
1244 = MCCXLIV
1245 = MCCXLV
1246 = MCCXLVI
1247 = MCCXLVII
1248 = MCCXLVIII
1249 = MCCXLIX
1250 = MCCL
1251 = MCCLI
1252 = MCCLII
1253 = MCCLIII
1254 = MCCLIV
1255 = MCCLV
1256 = MCCLVI
1257 = MCCLVII
1258 = MCCLVIII
1259 = MCCLIX
1260 = MCCLX
1261 = MCCLXI
1262 = MCCLXII
1263 = MCCLXIII
1264 = MCCLXIV
1265 = MCCLXV
1266 = MCCLXVI
1267 = MCCLXVII
1268 = MCCLXVIII
1269 = MCCLXIX
1270 = MCCLXX
1271 = MCCLXXI
1272 = MCCLXXII
1273 = MCCLXXIII
1274 = MCCLXXIV
1275 = MCCLXXV
1276 = MCCLXXVI
1277 = MCCLXXVII
1278 = MCCLXXVIII
1279 = MCCLXXIX
1280 = MCCLXXX
1281 = MCCLXXXI
1282 = MCCLXXXII
1283 = MCCLXXXIII
1284 = MCCLXXXIV
1285 = MCCLXXXV
1286 = MCCLXXXVI
1287 = MCCLXXXVII
1288 = MCCLXXXVIII
1289 = MCCLXXXIX
1290 = MCCXC
1291 = MCCXCI
1292 = MCCXCII
1293 = MCCXCIII
1294 = MCCXCIV
1295 = MCCXCV
1296 = MCCXCVI
1297 = MCCXCVII
1298 = MCCXCVIII
1299 = MCCXCIX
1300 = MCCC
1301 = MCCCI
1302 = MCCCII
1303 = MCCCIII
1304 = MCCCIV
1305 = MCCCV
1306 = MCCCVI
1307 = MCCCVII
1308 = MCCCVIII
1309 = MCCCIX
1310 = MCCCX
1311 = MCCCXI
1312 = MCCCXII
1313 = MCCCXIII
1314 = MCCCXIV
1315 = MCCCXV
1316 = MCCCXVI
1317 = MCCCXVII
1318 = MCCCXVIII
1319 = MCCCXIX
1320 = MCCCXX
1321 = MCCCXXI
1322 = MCCCXXII
1323 = MCCCXXIII
1324 = MCCCXXIV
1325 = MCCCXXV
1326 = MCCCXXVI
1327 = MCCCXXVII
1328 = MCCCXXVIII
1329 = MCCCXXIX
1330 = MCCCXXX
1331 = MCCCXXXI
1332 = MCCCXXXII
1333 = MCCCXXXIII
1334 = MCCCXXXIV
1335 = MCCCXXXV
1336 = MCCCXXXVI
1337 = MCCCXXXVII
1338 = MCCCXXXVIII
1339 = MCCCXXXIX
1340 = MCCCXL
1341 = MCCCXLI
1342 = MCCCXLII
1343 = MCCCXLIII
1344 = MCCCXLIV
1345 = MCCCXLV
1346 = MCCCXLVI
1347 = MCCCXLVII
1348 = MCCCXLVIII
1349 = MCCCXLIX
1350 = MCCCL
1351 = MCCCLI
1352 = MCCCLII
1353 = MCCCLIII
1354 = MCCCLIV
1355 = MCCCLV
1356 = MCCCLVI
1357 = MCCCLVII
1358 = MCCCLVIII
1359 = MCCCLIX
1360 = MCCCLX
1361 = MCCCLXI
1362 = MCCCLXII
1363 = MCCCLXIII
1364 = MCCCLXIV
1365 = MCCCLXV
1366 = MCCCLXVI
1367 = MCCCLXVII
1368 = MCCCLXVIII
1369 = MCCCLXIX
1370 = MCCCLXX
1371 = MCCCLXXI
1372 = MCCCLXXII
1373 = MCCCLXXIII
1374 = MCCCLXXIV
1375 = MCCCLXXV
1376 = MCCCLXXVI
1377 = MCCCLXXVII
1378 = MCCCLXXVIII
1379 = MCCCLXXIX
1380 = MCCCLXXX
1381 = MCCCLXXXI
1382 = MCCCLXXXII
1383 = MCCCLXXXIII
1384 = MCCCLXXXIV
1385 = MCCCLXXXV
1386 = MCCCLXXXVI
1387 = MCCCLXXXVII
1388 = MCCCLXXXVIII
1389 = MCCCLXXXIX
1390 = MCCCXC
1391 = MCCCXCI
1392 = MCCCXCII
1393 = MCCCXCIII
1394 = MCCCXCIV
1395 = MCCCXCV
1396 = MCCCXCVI
1397 = MCCCXCVII
1398 = MCCCXCVIII
1399 = MCCCXCIX
1400 = MCD
1401 = MCDI
1402 = MCDII
1403 = MCDIII
1404 = MCDIV
1405 = MCDV
1406 = MCDVI
1407 = MCDVII
1408 = MCDVIII
1409 = MCDIX
1410 = MCDX
1411 = MCDXI
1412 = MCDXII
1413 = MCDXIII
1414 = MCDXIV
1415 = MCDXV
1416 = MCDXVI
1417 = MCDXVII
1418 = MCDXVIII
1419 = MCDXIX
1420 = MCDXX
1421 = MCDXXI
1422 = MCDXXII
1423 = MCDXXIII
1424 = MCDXXIV
1425 = MCDXXV
1426 = MCDXXVI
1427 = MCDXXVII
1428 = MCDXXVIII
1429 = MCDXXIX
1430 = MCDXXX
1431 = MCDXXXI
1432 = MCDXXXII
1433 = MCDXXXIII
1434 = MCDXXXIV
1435 = MCDXXXV
1436 = MCDXXXVI
1437 = MCDXXXVII
1438 = MCDXXXVIII
1439 = MCDXXXIX
1440 = MCDXL
1441 = MCDXLI
1442 = MCDXLII
1443 = MCDXLIII
1444 = MCDXLIV
1445 = MCDXLV
1446 = MCDXLVI
1447 = MCDXLVII
1448 = MCDXLVIII
1449 = MCDXLIX
1450 = MCDL
1451 = MCDLI
1452 = MCDLII
1453 = MCDLIII
1454 = MCDLIV
1455 = MCDLV
1456 = MCDLVI
1457 = MCDLVII
1458 = MCDLVIII
1459 = MCDLIX
1460 = MCDLX
1461 = MCDLXI
1462 = MCDLXII
1463 = MCDLXIII
1464 = MCDLXIV
1465 = MCDLXV
1466 = MCDLXVI
1467 = MCDLXVII
1468 = MCDLXVIII
1469 = MCDLXIX
1470 = MCDLXX
1471 = MCDLXXI
1472 = MCDLXXII
1473 = MCDLXXIII
1474 = MCDLXXIV
1475 = MCDLXXV
1476 = MCDLXXVI
1477 = MCDLXXVII
1478 = MCDLXXVIII
1479 = MCDLXXIX
1480 = MCDLXXX
1481 = MCDLXXXI
1482 = MCDLXXXII
1483 = MCDLXXXIII
1484 = MCDLXXXIV
1485 = MCDLXXXV
1486 = MCDLXXXVI
1487 = MCDLXXXVII
1488 = MCDLXXXVIII
1489 = MCDLXXXIX
1490 = MCDXC
1491 = MCDXCI
1492 = MCDXCII
1493 = MCDXCIII
1494 = MCDXCIV
1495 = MCDXCV
1496 = MCDXCVI
1497 = MCDXCVII
1498 = MCDXCVIII
1499 = MCDXCIX
1500 = MD
1501 = MDI
1502 = MDII
1503 = MDIII
1504 = MDIV
1505 = MDV
1506 = MDVI
1507 = MDVII
1508 = MDVIII
1509 = MDIX
1510 = MDX
1511 = MDXI
1512 = MDXII
1513 = MDXIII
1514 = MDXIV
1515 = MDXV
1516 = MDXVI
1517 = MDXVII
1518 = MDXVIII
1519 = MDXIX
1520 = MDXX
1521 = MDXXI
1522 = MDXXII
1523 = MDXXIII
1524 = MDXXIV
1525 = MDXXV
1526 = MDXXVI
1527 = MDXXVII
1528 = MDXXVIII
1529 = MDXXIX
1530 = MDXXX
1531 = MDXXXI
1532 = MDXXXII
1533 = MDXXXIII
1534 = MDXXXIV
1535 = MDXXXV
1536 = MDXXXVI
1537 = MDXXXVII
1538 = MDXXXVIII
1539 = MDXXXIX
1540 = MDXL
1541 = MDXLI
1542 = MDXLII
1543 = MDXLIII
1544 = MDXLIV
1545 = MDXLV
1546 = MDXLVI
1547 = MDXLVII
1548 = MDXLVIII
1549 = MDXLIX
1550 = MDL
1551 = MDLI
1552 = MDLII
1553 = MDLIII
1554 = MDLIV
1555 = MDLV
1556 = MDLVI
1557 = MDLVII
1558 = MDLVIII
1559 = MDLIX
1560 = MDLX
1561 = MDLXI
1562 = MDLXII
1563 = MDLXIII
1564 = MDLXIV
1565 = MDLXV
1566 = MDLXVI
1567 = MDLXVII
1568 = MDLXVIII
1569 = MDLXIX
1570 = MDLXX
1571 = MDLXXI
1572 = MDLXXII
1573 = MDLXXIII
1574 = MDLXXIV
1575 = MDLXXV
1576 = MDLXXVI
1577 = MDLXXVII
1578 = MDLXXVIII
1579 = MDLXXIX
1580 = MDLXXX
1581 = MDLXXXI
1582 = MDLXXXII
1583 = MDLXXXIII
1584 = MDLXXXIV
1585 = MDLXXXV
1586 = MDLXXXVI
1587 = MDLXXXVII
1588 = MDLXXXVIII
1589 = MDLXXXIX
1590 = MDXC
1591 = MDXCI
1592 = MDXCII
1593 = MDXCIII
1594 = MDXCIV
1595 = MDXCV
1596 = MDXCVI
1597 = MDXCVII
1598 = MDXCVIII
1599 = MDXCIX
1600 = MDC
1601 = MDCI
1602 = MDCII
1603 = MDCIII
1604 = MDCIV
1605 = MDCV
1606 = MDCVI
1607 = MDCVII
1608 = MDCVIII
1609 = MDCIX
1610 = MDCX
1611 = MDCXI
1612 = MDCXII
1613 = MDCXIII
1614 = MDCXIV
1615 = MDCXV
1616 = MDCXVI
1617 = MDCXVII
1618 = MDCXVIII
1619 = MDCXIX
1620 = MDCXX
1621 = MDCXXI
1622 = MDCXXII
1623 = MDCXXIII
1624 = MDCXXIV
1625 = MDCXXV
1626 = MDCXXVI
1627 = MDCXXVII
1628 = MDCXXVIII
1629 = MDCXXIX
1630 = MDCXXX
1631 = MDCXXXI
1632 = MDCXXXII
1633 = MDCXXXIII
1634 = MDCXXXIV
1635 = MDCXXXV
1636 = MDCXXXVI
1637 = MDCXXXVII
1638 = MDCXXXVIII
1639 = MDCXXXIX
1640 = MDCXL
1641 = MDCXLI
1642 = MDCXLII
1643 = MDCXLIII
1644 = MDCXLIV
1645 = MDCXLV
1646 = MDCXLVI
1647 = MDCXLVII
1648 = MDCXLVIII
1649 = MDCXLIX
1650 = MDCL
1651 = MDCLI
1652 = MDCLII
1653 = MDCLIII
1654 = MDCLIV
1655 = MDCLV
1656 = MDCLVI
1657 = MDCLVII
1658 = MDCLVIII
1659 = MDCLIX
1660 = MDCLX
1661 = MDCLXI
1662 = MDCLXII
1663 = MDCLXIII
1664 = MDCLXIV
1665 = MDCLXV
1666 = MDCLXVI
1667 = MDCLXVII
1668 = MDCLXVIII
1669 = MDCLXIX
1670 = MDCLXX
1671 = MDCLXXI
1672 = MDCLXXII
1673 = MDCLXXIII
1674 = MDCLXXIV
1675 = MDCLXXV
1676 = MDCLXXVI
1677 = MDCLXXVII
1678 = MDCLXXVIII
1679 = MDCLXXIX
1680 = MDCLXXX
1681 = MDCLXXXI
1682 = MDCLXXXII
1683 = MDCLXXXIII
1684 = MDCLXXXIV
1685 = MDCLXXXV
1686 = MDCLXXXVI
1687 = MDCLXXXVII
1688 = MDCLXXXVIII
1689 = MDCLXXXIX
1690 = MDCXC
1691 = MDCXCI
1692 = MDCXCII
1693 = MDCXCIII
1694 = MDCXCIV
1695 = MDCXCV
1696 = MDCXCVI
1697 = MDCXCVII
1698 = MDCXCVIII
1699 = MDCXCIX
1700 = MDCC
1701 = MDCCI
1702 = MDCCII
1703 = MDCCIII
1704 = MDCCIV
1705 = MDCCV
1706 = MDCCVI
1707 = MDCCVII
1708 = MDCCVIII
1709 = MDCCIX
1710 = MDCCX
1711 = MDCCXI
1712 = MDCCXII
1713 = MDCCXIII
1714 = MDCCXIV
1715 = MDCCXV
1716 = MDCCXVI
1717 = MDCCXVII
1718 = MDCCXVIII
1719 = MDCCXIX
1720 = MDCCXX
1721 = MDCCXXI
1722 = MDCCXXII
1723 = MDCCXXIII
1724 = MDCCXXIV
1725 = MDCCXXV
1726 = MDCCXXVI
1727 = MDCCXXVII
1728 = MDCCXXVIII
1729 = MDCCXXIX
1730 = MDCCXXX
1731 = MDCCXXXI
1732 = MDCCXXXII
1733 = MDCCXXXIII
1734 = MDCCXXXIV
1735 = MDCCXXXV
1736 = MDCCXXXVI
1737 = MDCCXXXVII
1738 = MDCCXXXVIII
1739 = MDCCXXXIX
1740 = MDCCXL
1741 = MDCCXLI
1742 = MDCCXLII
1743 = MDCCXLIII
1744 = MDCCXLIV
1745 = MDCCXLV
1746 = MDCCXLVI
1747 = MDCCXLVII
1748 = MDCCXLVIII
1749 = MDCCXLIX
1750 = MDCCL
1751 = MDCCLI
1752 = MDCCLII
1753 = MDCCLIII
1754 = MDCCLIV
1755 = MDCCLV
1756 = MDCCLVI
1757 = MDCCLVII
1758 = MDCCLVIII
1759 = MDCCLIX
1760 = MDCCLX
1761 = MDCCLXI
1762 = MDCCLXII
1763 = MDCCLXIII
1764 = MDCCLXIV
1765 = MDCCLXV
1766 = MDCCLXVI
1767 = MDCCLXVII
1768 = MDCCLXVIII
1769 = MDCCLXIX
1770 = MDCCLXX
1771 = MDCCLXXI
1772 = MDCCLXXII
1773 = MDCCLXXIII
1774 = MDCCLXXIV
1775 = MDCCLXXV
1776 = MDCCLXXVI
1777 = MDCCLXXVII
1778 = MDCCLXXVIII
1779 = MDCCLXXIX
1780 = MDCCLXXX
1781 = MDCCLXXXI
1782 = MDCCLXXXII
1783 = MDCCLXXXIII
1784 = MDCCLXXXIV
1785 = MDCCLXXXV
1786 = MDCCLXXXVI
1787 = MDCCLXXXVII
1788 = MDCCLXXXVIII
1789 = MDCCLXXXIX
1790 = MDCCXC
1791 = MDCCXCI
1792 = MDCCXCII
1793 = MDCCXCIII
1794 = MDCCXCIV
1795 = MDCCXCV
1796 = MDCCXCVI
1797 = MDCCXCVII
1798 = MDCCXCVIII
1799 = MDCCXCIX
1800 = MDCCC
1801 = MDCCCI
1802 = MDCCCII
1803 = MDCCCIII
1804 = MDCCCIV
1805 = MDCCCV
1806 = MDCCCVI
1807 = MDCCCVII
1808 = MDCCCVIII
1809 = MDCCCIX
1810 = MDCCCX
1811 = MDCCCXI
1812 = MDCCCXII
1813 = MDCCCXIII
1814 = MDCCCXIV
1815 = MDCCCXV
1816 = MDCCCXVI
1817 = MDCCCXVII
1818 = MDCCCXVIII
1819 = MDCCCXIX
1820 = MDCCCXX
1821 = MDCCCXXI
1822 = MDCCCXXII
1823 = MDCCCXXIII
1824 = MDCCCXXIV
1825 = MDCCCXXV
1826 = MDCCCXXVI
1827 = MDCCCXXVII
1828 = MDCCCXXVIII
1829 = MDCCCXXIX
1830 = MDCCCXXX
1831 = MDCCCXXXI
1832 = MDCCCXXXII
1833 = MDCCCXXXIII
1834 = MDCCCXXXIV
1835 = MDCCCXXXV
1836 = MDCCCXXXVI
1837 = MDCCCXXXVII
1838 = MDCCCXXXVIII
1839 = MDCCCXXXIX
1840 = MDCCCXL
1841 = MDCCCXLI
1842 = MDCCCXLII
1843 = MDCCCXLIII
1844 = MDCCCXLIV
1845 = MDCCCXLV
1846 = MDCCCXLVI
1847 = MDCCCXLVII
1848 = MDCCCXLVIII
1849 = MDCCCXLIX
1850 = MDCCCL
1851 = MDCCCLI
1852 = MDCCCLII
1853 = MDCCCLIII
1854 = MDCCCLIV
1855 = MDCCCLV
1856 = MDCCCLVI
1857 = MDCCCLVII
1858 = MDCCCLVIII
1859 = MDCCCLIX
1860 = MDCCCLX
1861 = MDCCCLXI
1862 = MDCCCLXII
1863 = MDCCCLXIII
1864 = MDCCCLXIV
1865 = MDCCCLXV
1866 = MDCCCLXVI
1867 = MDCCCLXVII
1868 = MDCCCLXVIII
1869 = MDCCCLXIX
1870 = MDCCCLXX
1871 = MDCCCLXXI
1872 = MDCCCLXXII
1873 = MDCCCLXXIII
1874 = MDCCCLXXIV
1875 = MDCCCLXXV
1876 = MDCCCLXXVI
1877 = MDCCCLXXVII
1878 = MDCCCLXXVIII
1879 = MDCCCLXXIX
1880 = MDCCCLXXX
1881 = MDCCCLXXXI
1882 = MDCCCLXXXII
1883 = MDCCCLXXXIII
1884 = MDCCCLXXXIV
1885 = MDCCCLXXXV
1886 = MDCCCLXXXVI
1887 = MDCCCLXXXVII
1888 = MDCCCLXXXVIII
1889 = MDCCCLXXXIX
1890 = MDCCCXC
1891 = MDCCCXCI
1892 = MDCCCXCII
1893 = MDCCCXCIII
1894 = MDCCCXCIV
1895 = MDCCCXCV
1896 = MDCCCXCVI
1897 = MDCCCXCVII
1898 = MDCCCXCVIII
1899 = MDCCCXCIX
1900 = MCM
1901 = MCMI
1902 = MCMII
1903 = MCMIII
1904 = MCMIV
1905 = MCMV
1906 = MCMVI
1907 = MCMVII
1908 = MCMVIII
1909 = MCMIX
1910 = MCMX
1911 = MCMXI
1912 = MCMXII
1913 = MCMXIII
1914 = MCMXIV
1915 = MCMXV
1916 = MCMXVI
1917 = MCMXVII
1918 = MCMXVIII
1919 = MCMXIX
1920 = MCMXX
1921 = MCMXXI
1922 = MCMXXII
1923 = MCMXXIII
1924 = MCMXXIV
1925 = MCMXXV
1926 = MCMXXVI
1927 = MCMXXVII
1928 = MCMXXVIII
1929 = MCMXXIX
1930 = MCMXXX
1931 = MCMXXXI
1932 = MCMXXXII
1933 = MCMXXXIII
1934 = MCMXXXIV
1935 = MCMXXXV
1936 = MCMXXXVI
1937 = MCMXXXVII
1938 = MCMXXXVIII
1939 = MCMXXXIX
1940 = MCMXL
1941 = MCMXLI
1942 = MCMXLII
1943 = MCMXLIII
1944 = MCMXLIV
1945 = MCMXLV
1946 = MCMXLVI
1947 = MCMXLVII
1948 = MCMXLVIII
1949 = MCMXLIX
1950 = MCML
1951 = MCMLI
1952 = MCMLII
1953 = MCMLIII
1954 = MCMLIV
1955 = MCMLV
1956 = MCMLVI
1957 = MCMLVII
1958 = MCMLVIII
1959 = MCMLIX
1960 = MCMLX
1961 = MCMLXI
1962 = MCMLXII
1963 = MCMLXIII
1964 = MCMLXIV
1965 = MCMLXV
1966 = MCMLXVI
1967 = MCMLXVII
1968 = MCMLXVIII
1969 = MCMLXIX
1970 = MCMLXX
1971 = MCMLXXI
1972 = MCMLXXII
1973 = MCMLXXIII
1974 = MCMLXXIV
1975 = MCMLXXV
1976 = MCMLXXVI
1977 = MCMLXXVII
1978 = MCMLXXVIII
1979 = MCMLXXIX
1980 = MCMLXXX
1981 = MCMLXXXI
1982 = MCMLXXXII
1983 = MCMLXXXIII
1984 = MCMLXXXIV
1985 = MCMLXXXV
1986 = MCMLXXXVI
1987 = MCMLXXXVII
1988 = MCMLXXXVIII
1989 = MCMLXXXIX
1990 = MCMXC
1991 = MCMXCI
1992 = MCMXCII
1993 = MCMXCIII
1994 = MCMXCIV
1995 = MCMXCV
1996 = MCMXCVI
1997 = MCMXCVII
1998 = MCMXCVIII
1999 = MCMXCIX
2000 = MM
2001 = MMI
2002 = MMII
2003 = MMIII
2004 = MMIV
2005 = MMV
2006 = MMVI
2007 = MMVII
2008 = MMVIII
2009 = MMIX
2010 = MMX
2011 = MMXI
2012 = MMXII
2013 = MMXIII
2014 = MMXIV
2015 = MMXV
2016 = MMXVI
2017 = MMXVII
2018 = MMXVIII
2019 = MMXIX
2020 = MMXX
2021 = MMXXI
2022 = MMXXII
2023 = MMXXIII
2024 = MMXXIV
2025 = MMXXV
2026 = MMXXVI
2027 = MMXXVII
2028 = MMXXVIII
2029 = MMXXIX
2030 = MMXXX
2031 = MMXXXI
2032 = MMXXXII
2033 = MMXXXIII
2034 = MMXXXIV
2035 = MMXXXV
2036 = MMXXXVI
2037 = MMXXXVII
2038 = MMXXXVIII
2039 = MMXXXIX
2040 = MMXL
2041 = MMXLI
2042 = MMXLII
2043 = MMXLIII
2044 = MMXLIV
2045 = MMXLV
2046 = MMXLVI
2047 = MMXLVII
2048 = MMXLVIII
2049 = MMXLIX
2050 = MML
2051 = MMLI
2052 = MMLII
2053 = MMLIII
2054 = MMLIV
2055 = MMLV
2056 = MMLVI
2057 = MMLVII
2058 = MMLVIII
2059 = MMLIX
2060 = MMLX
2061 = MMLXI
2062 = MMLXII
2063 = MMLXIII
2064 = MMLXIV
2065 = MMLXV
2066 = MMLXVI
2067 = MMLXVII
2068 = MMLXVIII
2069 = MMLXIX
2070 = MMLXX
2071 = MMLXXI
2072 = MMLXXII
2073 = MMLXXIII
2074 = MMLXXIV
2075 = MMLXXV
2076 = MMLXXVI
2077 = MMLXXVII
2078 = MMLXXVIII
2079 = MMLXXIX
2080 = MMLXXX
2081 = MMLXXXI
2082 = MMLXXXII
2083 = MMLXXXIII
2084 = MMLXXXIV
2085 = MMLXXXV
2086 = MMLXXXVI
2087 = MMLXXXVII
2088 = MMLXXXVIII
2089 = MMLXXXIX
2090 = MMXC
2091 = MMXCI
2092 = MMXCII
2093 = MMXCIII
2094 = MMXCIV
2095 = MMXCV
2096 = MMXCVI
2097 = MMXCVII
2098 = MMXCVIII
2099 = MMXCIX
2100 = MMC
2101 = MMCI
2102 = MMCII
2103 = MMCIII
2104 = MMCIV
2105 = MMCV
2106 = MMCVI
2107 = MMCVII
2108 = MMCVIII
2109 = MMCIX
2110 = MMCX
2111 = MMCXI
2112 = MMCXII
2113 = MMCXIII
2114 = MMCXIV
2115 = MMCXV
2116 = MMCXVI
2117 = MMCXVII
2118 = MMCXVIII
2119 = MMCXIX
2120 = MMCXX
2121 = MMCXXI
2122 = MMCXXII
2123 = MMCXXIII
2124 = MMCXXIV
2125 = MMCXXV
2126 = MMCXXVI
2127 = MMCXXVII
2128 = MMCXXVIII
2129 = MMCXXIX
2130 = MMCXXX
2131 = MMCXXXI
2132 = MMCXXXII
2133 = MMCXXXIII
2134 = MMCXXXIV
2135 = MMCXXXV
2136 = MMCXXXVI
2137 = MMCXXXVII
2138 = MMCXXXVIII
2139 = MMCXXXIX
2140 = MMCXL
2141 = MMCXLI
2142 = MMCXLII
2143 = MMCXLIII
2144 = MMCXLIV
2145 = MMCXLV
2146 = MMCXLVI
2147 = MMCXLVII
2148 = MMCXLVIII
2149 = MMCXLIX
2150 = MMCL
2151 = MMCLI
2152 = MMCLII
2153 = MMCLIII
2154 = MMCLIV
2155 = MMCLV
2156 = MMCLVI
2157 = MMCLVII
2158 = MMCLVIII
2159 = MMCLIX
2160 = MMCLX
2161 = MMCLXI
2162 = MMCLXII
2163 = MMCLXIII
2164 = MMCLXIV
2165 = MMCLXV
2166 = MMCLXVI
2167 = MMCLXVII
2168 = MMCLXVIII
2169 = MMCLXIX
2170 = MMCLXX
2171 = MMCLXXI
2172 = MMCLXXII
2173 = MMCLXXIII
2174 = MMCLXXIV
2175 = MMCLXXV
2176 = MMCLXXVI
2177 = MMCLXXVII
2178 = MMCLXXVIII
2179 = MMCLXXIX
2180 = MMCLXXX
2181 = MMCLXXXI
2182 = MMCLXXXII
2183 = MMCLXXXIII
2184 = MMCLXXXIV
2185 = MMCLXXXV
2186 = MMCLXXXVI
2187 = MMCLXXXVII
2188 = MMCLXXXVIII
2189 = MMCLXXXIX
2190 = MMCXC
2191 = MMCXCI
2192 = MMCXCII
2193 = MMCXCIII
2194 = MMCXCIV
2195 = MMCXCV
2196 = MMCXCVI
2197 = MMCXCVII
2198 = MMCXCVIII
2199 = MMCXCIX
2200 = MMCC
2201 = MMCCI
2202 = MMCCII
2203 = MMCCIII
2204 = MMCCIV
2205 = MMCCV
2206 = MMCCVI
2207 = MMCCVII
2208 = MMCCVIII
2209 = MMCCIX
2210 = MMCCX
2211 = MMCCXI
2212 = MMCCXII
2213 = MMCCXIII
2214 = MMCCXIV
2215 = MMCCXV
2216 = MMCCXVI
2217 = MMCCXVII
2218 = MMCCXVIII
2219 = MMCCXIX
2220 = MMCCXX
2221 = MMCCXXI
2222 = MMCCXXII
2223 = MMCCXXIII
2224 = MMCCXXIV
2225 = MMCCXXV
2226 = MMCCXXVI
2227 = MMCCXXVII
2228 = MMCCXXVIII
2229 = MMCCXXIX
2230 = MMCCXXX
2231 = MMCCXXXI
2232 = MMCCXXXII
2233 = MMCCXXXIII
2234 = MMCCXXXIV
2235 = MMCCXXXV
2236 = MMCCXXXVI
2237 = MMCCXXXVII
2238 = MMCCXXXVIII
2239 = MMCCXXXIX
2240 = MMCCXL
2241 = MMCCXLI
2242 = MMCCXLII
2243 = MMCCXLIII
2244 = MMCCXLIV
2245 = MMCCXLV
2246 = MMCCXLVI
2247 = MMCCXLVII
2248 = MMCCXLVIII
2249 = MMCCXLIX
2250 = MMCCL
2251 = MMCCLI
2252 = MMCCLII
2253 = MMCCLIII
2254 = MMCCLIV
2255 = MMCCLV
2256 = MMCCLVI
2257 = MMCCLVII
2258 = MMCCLVIII
2259 = MMCCLIX
2260 = MMCCLX
2261 = MMCCLXI
2262 = MMCCLXII
2263 = MMCCLXIII
2264 = MMCCLXIV
2265 = MMCCLXV
2266 = MMCCLXVI
2267 = MMCCLXVII
2268 = MMCCLXVIII
2269 = MMCCLXIX
2270 = MMCCLXX
2271 = MMCCLXXI
2272 = MMCCLXXII
2273 = MMCCLXXIII
2274 = MMCCLXXIV
2275 = MMCCLXXV
2276 = MMCCLXXVI
2277 = MMCCLXXVII
2278 = MMCCLXXVIII
2279 = MMCCLXXIX
2280 = MMCCLXXX
2281 = MMCCLXXXI
2282 = MMCCLXXXII
2283 = MMCCLXXXIII
2284 = MMCCLXXXIV
2285 = MMCCLXXXV
2286 = MMCCLXXXVI
2287 = MMCCLXXXVII
2288 = MMCCLXXXVIII
2289 = MMCCLXXXIX
2290 = MMCCXC
2291 = MMCCXCI
2292 = MMCCXCII
2293 = MMCCXCIII
2294 = MMCCXCIV
2295 = MMCCXCV
2296 = MMCCXCVI
2297 = MMCCXCVII
2298 = MMCCXCVIII
2299 = MMCCXCIX
2300 = MMCCC
2301 = MMCCCI
2302 = MMCCCII
2303 = MMCCCIII
2304 = MMCCCIV
2305 = MMCCCV
2306 = MMCCCVI
2307 = MMCCCVII
2308 = MMCCCVIII
2309 = MMCCCIX
2310 = MMCCCX
2311 = MMCCCXI
2312 = MMCCCXII
2313 = MMCCCXIII
2314 = MMCCCXIV
2315 = MMCCCXV
2316 = MMCCCXVI
2317 = MMCCCXVII
2318 = MMCCCXVIII
2319 = MMCCCXIX
2320 = MMCCCXX
2321 = MMCCCXXI
2322 = MMCCCXXII
2323 = MMCCCXXIII
2324 = MMCCCXXIV
2325 = MMCCCXXV
2326 = MMCCCXXVI
2327 = MMCCCXXVII
2328 = MMCCCXXVIII
2329 = MMCCCXXIX
2330 = MMCCCXXX
2331 = MMCCCXXXI
2332 = MMCCCXXXII
2333 = MMCCCXXXIII
2334 = MMCCCXXXIV
2335 = MMCCCXXXV
2336 = MMCCCXXXVI
2337 = MMCCCXXXVII
2338 = MMCCCXXXVIII
2339 = MMCCCXXXIX
2340 = MMCCCXL
2341 = MMCCCXLI
2342 = MMCCCXLII
2343 = MMCCCXLIII
2344 = MMCCCXLIV
2345 = MMCCCXLV
2346 = MMCCCXLVI
2347 = MMCCCXLVII
2348 = MMCCCXLVIII
2349 = MMCCCXLIX
2350 = MMCCCL
2351 = MMCCCLI
2352 = MMCCCLII
2353 = MMCCCLIII
2354 = MMCCCLIV
2355 = MMCCCLV
2356 = MMCCCLVI
2357 = MMCCCLVII
2358 = MMCCCLVIII
2359 = MMCCCLIX
2360 = MMCCCLX
2361 = MMCCCLXI
2362 = MMCCCLXII
2363 = MMCCCLXIII
2364 = MMCCCLXIV
2365 = MMCCCLXV
2366 = MMCCCLXVI
2367 = MMCCCLXVII
2368 = MMCCCLXVIII
2369 = MMCCCLXIX
2370 = MMCCCLXX
2371 = MMCCCLXXI
2372 = MMCCCLXXII
2373 = MMCCCLXXIII
2374 = MMCCCLXXIV
2375 = MMCCCLXXV
2376 = MMCCCLXXVI
2377 = MMCCCLXXVII
2378 = MMCCCLXXVIII
2379 = MMCCCLXXIX
2380 = MMCCCLXXX
2381 = MMCCCLXXXI
2382 = MMCCCLXXXII
2383 = MMCCCLXXXIII
2384 = MMCCCLXXXIV
2385 = MMCCCLXXXV
2386 = MMCCCLXXXVI
2387 = MMCCCLXXXVII
2388 = MMCCCLXXXVIII
2389 = MMCCCLXXXIX
2390 = MMCCCXC
2391 = MMCCCXCI
2392 = MMCCCXCII
2393 = MMCCCXCIII
2394 = MMCCCXCIV
2395 = MMCCCXCV
2396 = MMCCCXCVI
2397 = MMCCCXCVII
2398 = MMCCCXCVIII
2399 = MMCCCXCIX
2400 = MMCD
2401 = MMCDI
2402 = MMCDII
2403 = MMCDIII
2404 = MMCDIV
2405 = MMCDV
2406 = MMCDVI
2407 = MMCDVII
2408 = MMCDVIII
2409 = MMCDIX
2410 = MMCDX
2411 = MMCDXI
2412 = MMCDXII
2413 = MMCDXIII
2414 = MMCDXIV
2415 = MMCDXV
2416 = MMCDXVI
2417 = MMCDXVII
2418 = MMCDXVIII
2419 = MMCDXIX
2420 = MMCDXX
2421 = MMCDXXI
2422 = MMCDXXII
2423 = MMCDXXIII
2424 = MMCDXXIV
2425 = MMCDXXV
2426 = MMCDXXVI
2427 = MMCDXXVII
2428 = MMCDXXVIII
2429 = MMCDXXIX
2430 = MMCDXXX
2431 = MMCDXXXI
2432 = MMCDXXXII
2433 = MMCDXXXIII
2434 = MMCDXXXIV
2435 = MMCDXXXV
2436 = MMCDXXXVI
2437 = MMCDXXXVII
2438 = MMCDXXXVIII
2439 = MMCDXXXIX
2440 = MMCDXL
2441 = MMCDXLI
2442 = MMCDXLII
2443 = MMCDXLIII
2444 = MMCDXLIV
2445 = MMCDXLV
2446 = MMCDXLVI
2447 = MMCDXLVII
2448 = MMCDXLVIII
2449 = MMCDXLIX
2450 = MMCDL
2451 = MMCDLI
2452 = MMCDLII
2453 = MMCDLIII
2454 = MMCDLIV
2455 = MMCDLV
2456 = MMCDLVI
2457 = MMCDLVII
2458 = MMCDLVIII
2459 = MMCDLIX
2460 = MMCDLX
2461 = MMCDLXI
2462 = MMCDLXII
2463 = MMCDLXIII
2464 = MMCDLXIV
2465 = MMCDLXV
2466 = MMCDLXVI
2467 = MMCDLXVII
2468 = MMCDLXVIII
2469 = MMCDLXIX
2470 = MMCDLXX
2471 = MMCDLXXI
2472 = MMCDLXXII
2473 = MMCDLXXIII
2474 = MMCDLXXIV
2475 = MMCDLXXV
2476 = MMCDLXXVI
2477 = MMCDLXXVII
2478 = MMCDLXXVIII
2479 = MMCDLXXIX
2480 = MMCDLXXX
2481 = MMCDLXXXI
2482 = MMCDLXXXII
2483 = MMCDLXXXIII
2484 = MMCDLXXXIV
2485 = MMCDLXXXV
2486 = MMCDLXXXVI
2487 = MMCDLXXXVII
2488 = MMCDLXXXVIII
2489 = MMCDLXXXIX
2490 = MMCDXC
2491 = MMCDXCI
2492 = MMCDXCII
2493 = MMCDXCIII
2494 = MMCDXCIV
2495 = MMCDXCV
2496 = MMCDXCVI
2497 = MMCDXCVII
2498 = MMCDXCVIII
2499 = MMCDXCIX
2500 = MMD
2501 = MMDI
2502 = MMDII
2503 = MMDIII
2504 = MMDIV
2505 = MMDV
2506 = MMDVI
2507 = MMDVII
2508 = MMDVIII
2509 = MMDIX
2510 = MMDX
2511 = MMDXI
2512 = MMDXII
2513 = MMDXIII
2514 = MMDXIV
2515 = MMDXV
2516 = MMDXVI
2517 = MMDXVII
2518 = MMDXVIII
2519 = MMDXIX
2520 = MMDXX
2521 = MMDXXI
2522 = MMDXXII
2523 = MMDXXIII
2524 = MMDXXIV
2525 = MMDXXV
2526 = MMDXXVI
2527 = MMDXXVII
2528 = MMDXXVIII
2529 = MMDXXIX
2530 = MMDXXX
2531 = MMDXXXI
2532 = MMDXXXII
2533 = MMDXXXIII
2534 = MMDXXXIV
2535 = MMDXXXV
2536 = MMDXXXVI
2537 = MMDXXXVII
2538 = MMDXXXVIII
2539 = MMDXXXIX
2540 = MMDXL
2541 = MMDXLI
2542 = MMDXLII
2543 = MMDXLIII
2544 = MMDXLIV
2545 = MMDXLV
2546 = MMDXLVI
2547 = MMDXLVII
2548 = MMDXLVIII
2549 = MMDXLIX
2550 = MMDL
2551 = MMDLI
2552 = MMDLII
2553 = MMDLIII
2554 = MMDLIV
2555 = MMDLV
2556 = MMDLVI
2557 = MMDLVII
2558 = MMDLVIII
2559 = MMDLIX
2560 = MMDLX
2561 = MMDLXI
2562 = MMDLXII
2563 = MMDLXIII
2564 = MMDLXIV
2565 = MMDLXV
2566 = MMDLXVI
2567 = MMDLXVII
2568 = MMDLXVIII
2569 = MMDLXIX
2570 = MMDLXX
2571 = MMDLXXI
2572 = MMDLXXII
2573 = MMDLXXIII
2574 = MMDLXXIV
2575 = MMDLXXV
2576 = MMDLXXVI
2577 = MMDLXXVII
2578 = MMDLXXVIII
2579 = MMDLXXIX
2580 = MMDLXXX
2581 = MMDLXXXI
2582 = MMDLXXXII
2583 = MMDLXXXIII
2584 = MMDLXXXIV
2585 = MMDLXXXV
2586 = MMDLXXXVI
2587 = MMDLXXXVII
2588 = MMDLXXXVIII
2589 = MMDLXXXIX
2590 = MMDXC
2591 = MMDXCI
2592 = MMDXCII
2593 = MMDXCIII
2594 = MMDXCIV
2595 = MMDXCV
2596 = MMDXCVI
2597 = MMDXCVII
2598 = MMDXCVIII
2599 = MMDXCIX
2600 = MMDC
2601 = MMDCI
2602 = MMDCII
2603 = MMDCIII
2604 = MMDCIV
2605 = MMDCV
2606 = MMDCVI
2607 = MMDCVII
2608 = MMDCVIII
2609 = MMDCIX
2610 = MMDCX
2611 = MMDCXI
2612 = MMDCXII
2613 = MMDCXIII
2614 = MMDCXIV
2615 = MMDCXV
2616 = MMDCXVI
2617 = MMDCXVII
2618 = MMDCXVIII
2619 = MMDCXIX
2620 = MMDCXX
2621 = MMDCXXI
2622 = MMDCXXII
2623 = MMDCXXIII
2624 = MMDCXXIV
2625 = MMDCXXV
2626 = MMDCXXVI
2627 = MMDCXXVII
2628 = MMDCXXVIII
2629 = MMDCXXIX
2630 = MMDCXXX
2631 = MMDCXXXI
2632 = MMDCXXXII
2633 = MMDCXXXIII
2634 = MMDCXXXIV
2635 = MMDCXXXV
2636 = MMDCXXXVI
2637 = MMDCXXXVII
2638 = MMDCXXXVIII
2639 = MMDCXXXIX
2640 = MMDCXL
2641 = MMDCXLI
2642 = MMDCXLII
2643 = MMDCXLIII
2644 = MMDCXLIV
2645 = MMDCXLV
2646 = MMDCXLVI
2647 = MMDCXLVII
2648 = MMDCXLVIII
2649 = MMDCXLIX
2650 = MMDCL
2651 = MMDCLI
2652 = MMDCLII
2653 = MMDCLIII
2654 = MMDCLIV
2655 = MMDCLV
2656 = MMDCLVI
2657 = MMDCLVII
2658 = MMDCLVIII
2659 = MMDCLIX
2660 = MMDCLX
2661 = MMDCLXI
2662 = MMDCLXII
2663 = MMDCLXIII
2664 = MMDCLXIV
2665 = MMDCLXV
2666 = MMDCLXVI
2667 = MMDCLXVII
2668 = MMDCLXVIII
2669 = MMDCLXIX
2670 = MMDCLXX
2671 = MMDCLXXI
2672 = MMDCLXXII
2673 = MMDCLXXIII
2674 = MMDCLXXIV
2675 = MMDCLXXV
2676 = MMDCLXXVI
2677 = MMDCLXXVII
2678 = MMDCLXXVIII
2679 = MMDCLXXIX
2680 = MMDCLXXX
2681 = MMDCLXXXI
2682 = MMDCLXXXII
2683 = MMDCLXXXIII
2684 = MMDCLXXXIV
2685 = MMDCLXXXV
2686 = MMDCLXXXVI
2687 = MMDCLXXXVII
2688 = MMDCLXXXVIII
2689 = MMDCLXXXIX
2690 = MMDCXC
2691 = MMDCXCI
2692 = MMDCXCII
2693 = MMDCXCIII
2694 = MMDCXCIV
2695 = MMDCXCV
2696 = MMDCXCVI
2697 = MMDCXCVII
2698 = MMDCXCVIII
2699 = MMDCXCIX
2700 = MMDCC
2701 = MMDCCI
2702 = MMDCCII
2703 = MMDCCIII
2704 = MMDCCIV
2705 = MMDCCV
2706 = MMDCCVI
2707 = MMDCCVII
2708 = MMDCCVIII
2709 = MMDCCIX
2710 = MMDCCX
2711 = MMDCCXI
2712 = MMDCCXII
2713 = MMDCCXIII
2714 = MMDCCXIV
2715 = MMDCCXV
2716 = MMDCCXVI
2717 = MMDCCXVII
2718 = MMDCCXVIII
2719 = MMDCCXIX
2720 = MMDCCXX
2721 = MMDCCXXI
2722 = MMDCCXXII
2723 = MMDCCXXIII
2724 = MMDCCXXIV
2725 = MMDCCXXV
2726 = MMDCCXXVI
2727 = MMDCCXXVII
2728 = MMDCCXXVIII
2729 = MMDCCXXIX
2730 = MMDCCXXX
2731 = MMDCCXXXI
2732 = MMDCCXXXII
2733 = MMDCCXXXIII
2734 = MMDCCXXXIV
2735 = MMDCCXXXV
2736 = MMDCCXXXVI
2737 = MMDCCXXXVII
2738 = MMDCCXXXVIII
2739 = MMDCCXXXIX
2740 = MMDCCXL
2741 = MMDCCXLI
2742 = MMDCCXLII
2743 = MMDCCXLIII
2744 = MMDCCXLIV
2745 = MMDCCXLV
2746 = MMDCCXLVI
2747 = MMDCCXLVII
2748 = MMDCCXLVIII
2749 = MMDCCXLIX
2750 = MMDCCL
2751 = MMDCCLI
2752 = MMDCCLII
2753 = MMDCCLIII
2754 = MMDCCLIV
2755 = MMDCCLV
2756 = MMDCCLVI
2757 = MMDCCLVII
2758 = MMDCCLVIII
2759 = MMDCCLIX
2760 = MMDCCLX
2761 = MMDCCLXI
2762 = MMDCCLXII
2763 = MMDCCLXIII
2764 = MMDCCLXIV
2765 = MMDCCLXV
2766 = MMDCCLXVI
2767 = MMDCCLXVII
2768 = MMDCCLXVIII
2769 = MMDCCLXIX
2770 = MMDCCLXX
2771 = MMDCCLXXI
2772 = MMDCCLXXII
2773 = MMDCCLXXIII
2774 = MMDCCLXXIV
2775 = MMDCCLXXV
2776 = MMDCCLXXVI
2777 = MMDCCLXXVII
2778 = MMDCCLXXVIII
2779 = MMDCCLXXIX
2780 = MMDCCLXXX
2781 = MMDCCLXXXI
2782 = MMDCCLXXXII
2783 = MMDCCLXXXIII
2784 = MMDCCLXXXIV
2785 = MMDCCLXXXV
2786 = MMDCCLXXXVI
2787 = MMDCCLXXXVII
2788 = MMDCCLXXXVIII
2789 = MMDCCLXXXIX
2790 = MMDCCXC
2791 = MMDCCXCI
2792 = MMDCCXCII
2793 = MMDCCXCIII
2794 = MMDCCXCIV
2795 = MMDCCXCV
2796 = MMDCCXCVI
2797 = MMDCCXCVII
2798 = MMDCCXCVIII
2799 = MMDCCXCIX
2800 = MMDCCC
2801 = MMDCCCI
2802 = MMDCCCII
2803 = MMDCCCIII
2804 = MMDCCCIV
2805 = MMDCCCV
2806 = MMDCCCVI
2807 = MMDCCCVII
2808 = MMDCCCVIII
2809 = MMDCCCIX
2810 = MMDCCCX
2811 = MMDCCCXI
2812 = MMDCCCXII
2813 = MMDCCCXIII
2814 = MMDCCCXIV
2815 = MMDCCCXV
2816 = MMDCCCXVI
2817 = MMDCCCXVII
2818 = MMDCCCXVIII
2819 = MMDCCCXIX
2820 = MMDCCCXX
2821 = MMDCCCXXI
2822 = MMDCCCXXII
2823 = MMDCCCXXIII
2824 = MMDCCCXXIV
2825 = MMDCCCXXV
2826 = MMDCCCXXVI
2827 = MMDCCCXXVII
2828 = MMDCCCXXVIII
2829 = MMDCCCXXIX
2830 = MMDCCCXXX
2831 = MMDCCCXXXI
2832 = MMDCCCXXXII
2833 = MMDCCCXXXIII
2834 = MMDCCCXXXIV
2835 = MMDCCCXXXV
2836 = MMDCCCXXXVI
2837 = MMDCCCXXXVII
2838 = MMDCCCXXXVIII
2839 = MMDCCCXXXIX
2840 = MMDCCCXL
2841 = MMDCCCXLI
2842 = MMDCCCXLII
2843 = MMDCCCXLIII
2844 = MMDCCCXLIV
2845 = MMDCCCXLV
2846 = MMDCCCXLVI
2847 = MMDCCCXLVII
2848 = MMDCCCXLVIII
2849 = MMDCCCXLIX
2850 = MMDCCCL
2851 = MMDCCCLI
2852 = MMDCCCLII
2853 = MMDCCCLIII
2854 = MMDCCCLIV
2855 = MMDCCCLV
2856 = MMDCCCLVI
2857 = MMDCCCLVII
2858 = MMDCCCLVIII
2859 = MMDCCCLIX
2860 = MMDCCCLX
2861 = MMDCCCLXI
2862 = MMDCCCLXII
2863 = MMDCCCLXIII
2864 = MMDCCCLXIV
2865 = MMDCCCLXV
2866 = MMDCCCLXVI
2867 = MMDCCCLXVII
2868 = MMDCCCLXVIII
2869 = MMDCCCLXIX
2870 = MMDCCCLXX
2871 = MMDCCCLXXI
2872 = MMDCCCLXXII
2873 = MMDCCCLXXIII
2874 = MMDCCCLXXIV
2875 = MMDCCCLXXV
2876 = MMDCCCLXXVI
2877 = MMDCCCLXXVII
2878 = MMDCCCLXXVIII
2879 = MMDCCCLXXIX
2880 = MMDCCCLXXX
2881 = MMDCCCLXXXI
2882 = MMDCCCLXXXII
2883 = MMDCCCLXXXIII
2884 = MMDCCCLXXXIV
2885 = MMDCCCLXXXV
2886 = MMDCCCLXXXVI
2887 = MMDCCCLXXXVII
2888 = MMDCCCLXXXVIII
2889 = MMDCCCLXXXIX
2890 = MMDCCCXC
2891 = MMDCCCXCI
2892 = MMDCCCXCII
2893 = MMDCCCXCIII
2894 = MMDCCCXCIV
2895 = MMDCCCXCV
2896 = MMDCCCXCVI
2897 = MMDCCCXCVII
2898 = MMDCCCXCVIII
2899 = MMDCCCXCIX
2900 = MMCM
2901 = MMCMI
2902 = MMCMII
2903 = MMCMIII
2904 = MMCMIV
2905 = MMCMV
2906 = MMCMVI
2907 = MMCMVII
2908 = MMCMVIII
2909 = MMCMIX
2910 = MMCMX
2911 = MMCMXI
2912 = MMCMXII
2913 = MMCMXIII
2914 = MMCMXIV
2915 = MMCMXV
2916 = MMCMXVI
2917 = MMCMXVII
2918 = MMCMXVIII
2919 = MMCMXIX
2920 = MMCMXX
2921 = MMCMXXI
2922 = MMCMXXII
2923 = MMCMXXIII
2924 = MMCMXXIV
2925 = MMCMXXV
2926 = MMCMXXVI
2927 = MMCMXXVII
2928 = MMCMXXVIII
2929 = MMCMXXIX
2930 = MMCMXXX
2931 = MMCMXXXI
2932 = MMCMXXXII
2933 = MMCMXXXIII
2934 = MMCMXXXIV
2935 = MMCMXXXV
2936 = MMCMXXXVI
2937 = MMCMXXXVII
2938 = MMCMXXXVIII
2939 = MMCMXXXIX
2940 = MMCMXL
2941 = MMCMXLI
2942 = MMCMXLII
2943 = MMCMXLIII
2944 = MMCMXLIV
2945 = MMCMXLV
2946 = MMCMXLVI
2947 = MMCMXLVII
2948 = MMCMXLVIII
2949 = MMCMXLIX
2950 = MMCML
2951 = MMCMLI
2952 = MMCMLII
2953 = MMCMLIII
2954 = MMCMLIV
2955 = MMCMLV
2956 = MMCMLVI
2957 = MMCMLVII
2958 = MMCMLVIII
2959 = MMCMLIX
2960 = MMCMLX
2961 = MMCMLXI
2962 = MMCMLXII
2963 = MMCMLXIII
2964 = MMCMLXIV
2965 = MMCMLXV
2966 = MMCMLXVI
2967 = MMCMLXVII
2968 = MMCMLXVIII
2969 = MMCMLXIX
2970 = MMCMLXX
2971 = MMCMLXXI
2972 = MMCMLXXII
2973 = MMCMLXXIII
2974 = MMCMLXXIV
2975 = MMCMLXXV
2976 = MMCMLXXVI
2977 = MMCMLXXVII
2978 = MMCMLXXVIII
2979 = MMCMLXXIX
2980 = MMCMLXXX
2981 = MMCMLXXXI
2982 = MMCMLXXXII
2983 = MMCMLXXXIII
2984 = MMCMLXXXIV
2985 = MMCMLXXXV
2986 = MMCMLXXXVI
2987 = MMCMLXXXVII
2988 = MMCMLXXXVIII
2989 = MMCMLXXXIX
2990 = MMCMXC
2991 = MMCMXCI
2992 = MMCMXCII
2993 = MMCMXCIII
2994 = MMCMXCIV
2995 = MMCMXCV
2996 = MMCMXCVI
2997 = MMCMXCVII
2998 = MMCMXCVIII
2999 = MMCMXCIX
3000 = MMM
3001 = MMMI
3002 = MMMII
3003 = MMMIII
3004 = MMMIV
3005 = MMMV
3006 = MMMVI
3007 = MMMVII
3008 = MMMVIII
3009 = MMMIX
3010 = MMMX
3011 = MMMXI
3012 = MMMXII
3013 = MMMXIII
3014 = MMMXIV
3015 = MMMXV
3016 = MMMXVI
3017 = MMMXVII
3018 = MMMXVIII
3019 = MMMXIX
3020 = MMMXX
3021 = MMMXXI
3022 = MMMXXII
3023 = MMMXXIII
3024 = MMMXXIV
3025 = MMMXXV
3026 = MMMXXVI
3027 = MMMXXVII
3028 = MMMXXVIII
3029 = MMMXXIX
3030 = MMMXXX
3031 = MMMXXXI
3032 = MMMXXXII
3033 = MMMXXXIII
3034 = MMMXXXIV
3035 = MMMXXXV
3036 = MMMXXXVI
3037 = MMMXXXVII
3038 = MMMXXXVIII
3039 = MMMXXXIX
3040 = MMMXL
3041 = MMMXLI
3042 = MMMXLII
3043 = MMMXLIII
3044 = MMMXLIV
3045 = MMMXLV
3046 = MMMXLVI
3047 = MMMXLVII
3048 = MMMXLVIII
3049 = MMMXLIX
3050 = MMML
3051 = MMMLI
3052 = MMMLII
3053 = MMMLIII
3054 = MMMLIV
3055 = MMMLV
3056 = MMMLVI
3057 = MMMLVII
3058 = MMMLVIII
3059 = MMMLIX
3060 = MMMLX
3061 = MMMLXI
3062 = MMMLXII
3063 = MMMLXIII
3064 = MMMLXIV
3065 = MMMLXV
3066 = MMMLXVI
3067 = MMMLXVII
3068 = MMMLXVIII
3069 = MMMLXIX
3070 = MMMLXX
3071 = MMMLXXI
3072 = MMMLXXII
3073 = MMMLXXIII
3074 = MMMLXXIV
3075 = MMMLXXV
3076 = MMMLXXVI
3077 = MMMLXXVII
3078 = MMMLXXVIII
3079 = MMMLXXIX
3080 = MMMLXXX
3081 = MMMLXXXI
3082 = MMMLXXXII
3083 = MMMLXXXIII
3084 = MMMLXXXIV
3085 = MMMLXXXV
3086 = MMMLXXXVI
3087 = MMMLXXXVII
3088 = MMMLXXXVIII
3089 = MMMLXXXIX
3090 = MMMXC
3091 = MMMXCI
3092 = MMMXCII
3093 = MMMXCIII
3094 = MMMXCIV
3095 = MMMXCV
3096 = MMMXCVI
3097 = MMMXCVII
3098 = MMMXCVIII
3099 = MMMXCIX
3100 = MMMC
3101 = MMMCI
3102 = MMMCII
3103 = MMMCIII
3104 = MMMCIV
3105 = MMMCV
3106 = MMMCVI
3107 = MMMCVII
3108 = MMMCVIII
3109 = MMMCIX
3110 = MMMCX
3111 = MMMCXI
3112 = MMMCXII
3113 = MMMCXIII
3114 = MMMCXIV
3115 = MMMCXV
3116 = MMMCXVI
3117 = MMMCXVII
3118 = MMMCXVIII
3119 = MMMCXIX
3120 = MMMCXX
3121 = MMMCXXI
3122 = MMMCXXII
3123 = MMMCXXIII
3124 = MMMCXXIV
3125 = MMMCXXV
3126 = MMMCXXVI
3127 = MMMCXXVII
3128 = MMMCXXVIII
3129 = MMMCXXIX
3130 = MMMCXXX
3131 = MMMCXXXI
3132 = MMMCXXXII
3133 = MMMCXXXIII
3134 = MMMCXXXIV
3135 = MMMCXXXV
3136 = MMMCXXXVI
3137 = MMMCXXXVII
3138 = MMMCXXXVIII
3139 = MMMCXXXIX
3140 = MMMCXL
3141 = MMMCXLI
3142 = MMMCXLII
3143 = MMMCXLIII
3144 = MMMCXLIV
3145 = MMMCXLV
3146 = MMMCXLVI
3147 = MMMCXLVII
3148 = MMMCXLVIII
3149 = MMMCXLIX
3150 = MMMCL
3151 = MMMCLI
3152 = MMMCLII
3153 = MMMCLIII
3154 = MMMCLIV
3155 = MMMCLV
3156 = MMMCLVI
3157 = MMMCLVII
3158 = MMMCLVIII
3159 = MMMCLIX
3160 = MMMCLX
3161 = MMMCLXI
3162 = MMMCLXII
3163 = MMMCLXIII
3164 = MMMCLXIV
3165 = MMMCLXV
3166 = MMMCLXVI
3167 = MMMCLXVII
3168 = MMMCLXVIII
3169 = MMMCLXIX
3170 = MMMCLXX
3171 = MMMCLXXI
3172 = MMMCLXXII
3173 = MMMCLXXIII
3174 = MMMCLXXIV
3175 = MMMCLXXV
3176 = MMMCLXXVI
3177 = MMMCLXXVII
3178 = MMMCLXXVIII
3179 = MMMCLXXIX
3180 = MMMCLXXX
3181 = MMMCLXXXI
3182 = MMMCLXXXII
3183 = MMMCLXXXIII
3184 = MMMCLXXXIV
3185 = MMMCLXXXV
3186 = MMMCLXXXVI
3187 = MMMCLXXXVII
3188 = MMMCLXXXVIII
3189 = MMMCLXXXIX
3190 = MMMCXC
3191 = MMMCXCI
3192 = MMMCXCII
3193 = MMMCXCIII
3194 = MMMCXCIV
3195 = MMMCXCV
3196 = MMMCXCVI
3197 = MMMCXCVII
3198 = MMMCXCVIII
3199 = MMMCXCIX
3200 = MMMCC
3201 = MMMCCI
3202 = MMMCCII
3203 = MMMCCIII
3204 = MMMCCIV
3205 = MMMCCV
3206 = MMMCCVI
3207 = MMMCCVII
3208 = MMMCCVIII
3209 = MMMCCIX
3210 = MMMCCX
3211 = MMMCCXI
3212 = MMMCCXII
3213 = MMMCCXIII
3214 = MMMCCXIV
3215 = MMMCCXV
3216 = MMMCCXVI
3217 = MMMCCXVII
3218 = MMMCCXVIII
3219 = MMMCCXIX
3220 = MMMCCXX
3221 = MMMCCXXI
3222 = MMMCCXXII
3223 = MMMCCXXIII
3224 = MMMCCXXIV
3225 = MMMCCXXV
3226 = MMMCCXXVI
3227 = MMMCCXXVII
3228 = MMMCCXXVIII
3229 = MMMCCXXIX
3230 = MMMCCXXX
3231 = MMMCCXXXI
3232 = MMMCCXXXII
3233 = MMMCCXXXIII
3234 = MMMCCXXXIV
3235 = MMMCCXXXV
3236 = MMMCCXXXVI
3237 = MMMCCXXXVII
3238 = MMMCCXXXVIII
3239 = MMMCCXXXIX
3240 = MMMCCXL
3241 = MMMCCXLI
3242 = MMMCCXLII
3243 = MMMCCXLIII
3244 = MMMCCXLIV
3245 = MMMCCXLV
3246 = MMMCCXLVI
3247 = MMMCCXLVII
3248 = MMMCCXLVIII
3249 = MMMCCXLIX
3250 = MMMCCL
3251 = MMMCCLI
3252 = MMMCCLII
3253 = MMMCCLIII
3254 = MMMCCLIV
3255 = MMMCCLV
3256 = MMMCCLVI
3257 = MMMCCLVII
3258 = MMMCCLVIII
3259 = MMMCCLIX
3260 = MMMCCLX
3261 = MMMCCLXI
3262 = MMMCCLXII
3263 = MMMCCLXIII
3264 = MMMCCLXIV
3265 = MMMCCLXV
3266 = MMMCCLXVI
3267 = MMMCCLXVII
3268 = MMMCCLXVIII
3269 = MMMCCLXIX
3270 = MMMCCLXX
3271 = MMMCCLXXI
3272 = MMMCCLXXII
3273 = MMMCCLXXIII
3274 = MMMCCLXXIV
3275 = MMMCCLXXV
3276 = MMMCCLXXVI
3277 = MMMCCLXXVII
3278 = MMMCCLXXVIII
3279 = MMMCCLXXIX
3280 = MMMCCLXXX
3281 = MMMCCLXXXI
3282 = MMMCCLXXXII
3283 = MMMCCLXXXIII
3284 = MMMCCLXXXIV
3285 = MMMCCLXXXV
3286 = MMMCCLXXXVI
3287 = MMMCCLXXXVII
3288 = MMMCCLXXXVIII
3289 = MMMCCLXXXIX
3290 = MMMCCXC
3291 = MMMCCXCI
3292 = MMMCCXCII
3293 = MMMCCXCIII
3294 = MMMCCXCIV
3295 = MMMCCXCV
3296 = MMMCCXCVI
3297 = MMMCCXCVII
3298 = MMMCCXCVIII
3299 = MMMCCXCIX
3300 = MMMCCC
3301 = MMMCCCI
3302 = MMMCCCII
3303 = MMMCCCIII
3304 = MMMCCCIV
3305 = MMMCCCV
3306 = MMMCCCVI
3307 = MMMCCCVII
3308 = MMMCCCVIII
3309 = MMMCCCIX
3310 = MMMCCCX
3311 = MMMCCCXI
3312 = MMMCCCXII
3313 = MMMCCCXIII
3314 = MMMCCCXIV
3315 = MMMCCCXV
3316 = MMMCCCXVI
3317 = MMMCCCXVII
3318 = MMMCCCXVIII
3319 = MMMCCCXIX
3320 = MMMCCCXX
3321 = MMMCCCXXI
3322 = MMMCCCXXII
3323 = MMMCCCXXIII
3324 = MMMCCCXXIV
3325 = MMMCCCXXV
3326 = MMMCCCXXVI
3327 = MMMCCCXXVII
3328 = MMMCCCXXVIII
3329 = MMMCCCXXIX
3330 = MMMCCCXXX
3331 = MMMCCCXXXI
3332 = MMMCCCXXXII
3333 = MMMCCCXXXIII
3334 = MMMCCCXXXIV
3335 = MMMCCCXXXV
3336 = MMMCCCXXXVI
3337 = MMMCCCXXXVII
3338 = MMMCCCXXXVIII
3339 = MMMCCCXXXIX
3340 = MMMCCCXL
3341 = MMMCCCXLI
3342 = MMMCCCXLII
3343 = MMMCCCXLIII
3344 = MMMCCCXLIV
3345 = MMMCCCXLV
3346 = MMMCCCXLVI
3347 = MMMCCCXLVII
3348 = MMMCCCXLVIII
3349 = MMMCCCXLIX
3350 = MMMCCCL
3351 = MMMCCCLI
3352 = MMMCCCLII
3353 = MMMCCCLIII
3354 = MMMCCCLIV
3355 = MMMCCCLV
3356 = MMMCCCLVI
3357 = MMMCCCLVII
3358 = MMMCCCLVIII
3359 = MMMCCCLIX
3360 = MMMCCCLX
3361 = MMMCCCLXI
3362 = MMMCCCLXII
3363 = MMMCCCLXIII
3364 = MMMCCCLXIV
3365 = MMMCCCLXV
3366 = MMMCCCLXVI
3367 = MMMCCCLXVII
3368 = MMMCCCLXVIII
3369 = MMMCCCLXIX
3370 = MMMCCCLXX
3371 = MMMCCCLXXI
3372 = MMMCCCLXXII
3373 = MMMCCCLXXIII
3374 = MMMCCCLXXIV
3375 = MMMCCCLXXV
3376 = MMMCCCLXXVI
3377 = MMMCCCLXXVII
3378 = MMMCCCLXXVIII
3379 = MMMCCCLXXIX
3380 = MMMCCCLXXX
3381 = MMMCCCLXXXI
3382 = MMMCCCLXXXII
3383 = MMMCCCLXXXIII
3384 = MMMCCCLXXXIV
3385 = MMMCCCLXXXV
3386 = MMMCCCLXXXVI
3387 = MMMCCCLXXXVII
3388 = MMMCCCLXXXVIII
3389 = MMMCCCLXXXIX
3390 = MMMCCCXC
3391 = MMMCCCXCI
3392 = MMMCCCXCII
3393 = MMMCCCXCIII
3394 = MMMCCCXCIV
3395 = MMMCCCXCV
3396 = MMMCCCXCVI
3397 = MMMCCCXCVII
3398 = MMMCCCXCVIII
3399 = MMMCCCXCIX
3400 = MMMCD
3401 = MMMCDI
3402 = MMMCDII
3403 = MMMCDIII
3404 = MMMCDIV
3405 = MMMCDV
3406 = MMMCDVI
3407 = MMMCDVII
3408 = MMMCDVIII
3409 = MMMCDIX
3410 = MMMCDX
3411 = MMMCDXI
3412 = MMMCDXII
3413 = MMMCDXIII
3414 = MMMCDXIV
3415 = MMMCDXV
3416 = MMMCDXVI
3417 = MMMCDXVII
3418 = MMMCDXVIII
3419 = MMMCDXIX
3420 = MMMCDXX
3421 = MMMCDXXI
3422 = MMMCDXXII
3423 = MMMCDXXIII
3424 = MMMCDXXIV
3425 = MMMCDXXV
3426 = MMMCDXXVI
3427 = MMMCDXXVII
3428 = MMMCDXXVIII
3429 = MMMCDXXIX
3430 = MMMCDXXX
3431 = MMMCDXXXI
3432 = MMMCDXXXII
3433 = MMMCDXXXIII
3434 = MMMCDXXXIV
3435 = MMMCDXXXV
3436 = MMMCDXXXVI
3437 = MMMCDXXXVII
3438 = MMMCDXXXVIII
3439 = MMMCDXXXIX
3440 = MMMCDXL
3441 = MMMCDXLI
3442 = MMMCDXLII
3443 = MMMCDXLIII
3444 = MMMCDXLIV
3445 = MMMCDXLV
3446 = MMMCDXLVI
3447 = MMMCDXLVII
3448 = MMMCDXLVIII
3449 = MMMCDXLIX
3450 = MMMCDL
3451 = MMMCDLI
3452 = MMMCDLII
3453 = MMMCDLIII
3454 = MMMCDLIV
3455 = MMMCDLV
3456 = MMMCDLVI
3457 = MMMCDLVII
3458 = MMMCDLVIII
3459 = MMMCDLIX
3460 = MMMCDLX
3461 = MMMCDLXI
3462 = MMMCDLXII
3463 = MMMCDLXIII
3464 = MMMCDLXIV
3465 = MMMCDLXV
3466 = MMMCDLXVI
3467 = MMMCDLXVII
3468 = MMMCDLXVIII
3469 = MMMCDLXIX
3470 = MMMCDLXX
3471 = MMMCDLXXI
3472 = MMMCDLXXII
3473 = MMMCDLXXIII
3474 = MMMCDLXXIV
3475 = MMMCDLXXV
3476 = MMMCDLXXVI
3477 = MMMCDLXXVII
3478 = MMMCDLXXVIII
3479 = MMMCDLXXIX
3480 = MMMCDLXXX
3481 = MMMCDLXXXI
3482 = MMMCDLXXXII
3483 = MMMCDLXXXIII
3484 = MMMCDLXXXIV
3485 = MMMCDLXXXV
3486 = MMMCDLXXXVI
3487 = MMMCDLXXXVII
3488 = MMMCDLXXXVIII
3489 = MMMCDLXXXIX
3490 = MMMCDXC
3491 = MMMCDXCI
3492 = MMMCDXCII
3493 = MMMCDXCIII
3494 = MMMCDXCIV
3495 = MMMCDXCV
3496 = MMMCDXCVI
3497 = MMMCDXCVII
3498 = MMMCDXCVIII
3499 = MMMCDXCIX
3500 = MMMD
3501 = MMMDI
3502 = MMMDII
3503 = MMMDIII
3504 = MMMDIV
3505 = MMMDV
3506 = MMMDVI
3507 = MMMDVII
3508 = MMMDVIII
3509 = MMMDIX
3510 = MMMDX
3511 = MMMDXI
3512 = MMMDXII
3513 = MMMDXIII
3514 = MMMDXIV
3515 = MMMDXV
3516 = MMMDXVI
3517 = MMMDXVII
3518 = MMMDXVIII
3519 = MMMDXIX
3520 = MMMDXX
3521 = MMMDXXI
3522 = MMMDXXII
3523 = MMMDXXIII
3524 = MMMDXXIV
3525 = MMMDXXV
3526 = MMMDXXVI
3527 = MMMDXXVII
3528 = MMMDXXVIII
3529 = MMMDXXIX
3530 = MMMDXXX
3531 = MMMDXXXI
3532 = MMMDXXXII
3533 = MMMDXXXIII
3534 = MMMDXXXIV
3535 = MMMDXXXV
3536 = MMMDXXXVI
3537 = MMMDXXXVII
3538 = MMMDXXXVIII
3539 = MMMDXXXIX
3540 = MMMDXL
3541 = MMMDXLI
3542 = MMMDXLII
3543 = MMMDXLIII
3544 = MMMDXLIV
3545 = MMMDXLV
3546 = MMMDXLVI
3547 = MMMDXLVII
3548 = MMMDXLVIII
3549 = MMMDXLIX
3550 = MMMDL
3551 = MMMDLI
3552 = MMMDLII
3553 = MMMDLIII
3554 = MMMDLIV
3555 = MMMDLV
3556 = MMMDLVI
3557 = MMMDLVII
3558 = MMMDLVIII
3559 = MMMDLIX
3560 = MMMDLX
3561 = MMMDLXI
3562 = MMMDLXII
3563 = MMMDLXIII
3564 = MMMDLXIV
3565 = MMMDLXV
3566 = MMMDLXVI
3567 = MMMDLXVII
3568 = MMMDLXVIII
3569 = MMMDLXIX
3570 = MMMDLXX
3571 = MMMDLXXI
3572 = MMMDLXXII
3573 = MMMDLXXIII
3574 = MMMDLXXIV
3575 = MMMDLXXV
3576 = MMMDLXXVI
3577 = MMMDLXXVII
3578 = MMMDLXXVIII
3579 = MMMDLXXIX
3580 = MMMDLXXX
3581 = MMMDLXXXI
3582 = MMMDLXXXII
3583 = MMMDLXXXIII
3584 = MMMDLXXXIV
3585 = MMMDLXXXV
3586 = MMMDLXXXVI
3587 = MMMDLXXXVII
3588 = MMMDLXXXVIII
3589 = MMMDLXXXIX
3590 = MMMDXC
3591 = MMMDXCI
3592 = MMMDXCII
3593 = MMMDXCIII
3594 = MMMDXCIV
3595 = MMMDXCV
3596 = MMMDXCVI
3597 = MMMDXCVII
3598 = MMMDXCVIII
3599 = MMMDXCIX
3600 = MMMDC
3601 = MMMDCI
3602 = MMMDCII
3603 = MMMDCIII
3604 = MMMDCIV
3605 = MMMDCV
3606 = MMMDCVI
3607 = MMMDCVII
3608 = MMMDCVIII
3609 = MMMDCIX
3610 = MMMDCX
3611 = MMMDCXI
3612 = MMMDCXII
3613 = MMMDCXIII
3614 = MMMDCXIV
3615 = MMMDCXV
3616 = MMMDCXVI
3617 = MMMDCXVII
3618 = MMMDCXVIII
3619 = MMMDCXIX
3620 = MMMDCXX
3621 = MMMDCXXI
3622 = MMMDCXXII
3623 = MMMDCXXIII
3624 = MMMDCXXIV
3625 = MMMDCXXV
3626 = MMMDCXXVI
3627 = MMMDCXXVII
3628 = MMMDCXXVIII
3629 = MMMDCXXIX
3630 = MMMDCXXX
3631 = MMMDCXXXI
3632 = MMMDCXXXII
3633 = MMMDCXXXIII
3634 = MMMDCXXXIV
3635 = MMMDCXXXV
3636 = MMMDCXXXVI
3637 = MMMDCXXXVII
3638 = MMMDCXXXVIII
3639 = MMMDCXXXIX
3640 = MMMDCXL
3641 = MMMDCXLI
3642 = MMMDCXLII
3643 = MMMDCXLIII
3644 = MMMDCXLIV
3645 = MMMDCXLV
3646 = MMMDCXLVI
3647 = MMMDCXLVII
3648 = MMMDCXLVIII
3649 = MMMDCXLIX
3650 = MMMDCL
3651 = MMMDCLI
3652 = MMMDCLII
3653 = MMMDCLIII
3654 = MMMDCLIV
3655 = MMMDCLV
3656 = MMMDCLVI
3657 = MMMDCLVII
3658 = MMMDCLVIII
3659 = MMMDCLIX
3660 = MMMDCLX
3661 = MMMDCLXI
3662 = MMMDCLXII
3663 = MMMDCLXIII
3664 = MMMDCLXIV
3665 = MMMDCLXV
3666 = MMMDCLXVI
3667 = MMMDCLXVII
3668 = MMMDCLXVIII
3669 = MMMDCLXIX
3670 = MMMDCLXX
3671 = MMMDCLXXI
3672 = MMMDCLXXII
3673 = MMMDCLXXIII
3674 = MMMDCLXXIV
3675 = MMMDCLXXV
3676 = MMMDCLXXVI
3677 = MMMDCLXXVII
3678 = MMMDCLXXVIII
3679 = MMMDCLXXIX
3680 = MMMDCLXXX
3681 = MMMDCLXXXI
3682 = MMMDCLXXXII
3683 = MMMDCLXXXIII
3684 = MMMDCLXXXIV
3685 = MMMDCLXXXV
3686 = MMMDCLXXXVI
3687 = MMMDCLXXXVII
3688 = MMMDCLXXXVIII
3689 = MMMDCLXXXIX
3690 = MMMDCXC
3691 = MMMDCXCI
3692 = MMMDCXCII
3693 = MMMDCXCIII
3694 = MMMDCXCIV
3695 = MMMDCXCV
3696 = MMMDCXCVI
3697 = MMMDCXCVII
3698 = MMMDCXCVIII
3699 = MMMDCXCIX
3700 = MMMDCC
3701 = MMMDCCI
3702 = MMMDCCII
3703 = MMMDCCIII
3704 = MMMDCCIV
3705 = MMMDCCV
3706 = MMMDCCVI
3707 = MMMDCCVII
3708 = MMMDCCVIII
3709 = MMMDCCIX
3710 = MMMDCCX
3711 = MMMDCCXI
3712 = MMMDCCXII
3713 = MMMDCCXIII
3714 = MMMDCCXIV
3715 = MMMDCCXV
3716 = MMMDCCXVI
3717 = MMMDCCXVII
3718 = MMMDCCXVIII
3719 = MMMDCCXIX
3720 = MMMDCCXX
3721 = MMMDCCXXI
3722 = MMMDCCXXII
3723 = MMMDCCXXIII
3724 = MMMDCCXXIV
3725 = MMMDCCXXV
3726 = MMMDCCXXVI
3727 = MMMDCCXXVII
3728 = MMMDCCXXVIII
3729 = MMMDCCXXIX
3730 = MMMDCCXXX
3731 = MMMDCCXXXI
3732 = MMMDCCXXXII
3733 = MMMDCCXXXIII
3734 = MMMDCCXXXIV
3735 = MMMDCCXXXV
3736 = MMMDCCXXXVI
3737 = MMMDCCXXXVII
3738 = MMMDCCXXXVIII
3739 = MMMDCCXXXIX
3740 = MMMDCCXL
3741 = MMMDCCXLI
3742 = MMMDCCXLII
3743 = MMMDCCXLIII
3744 = MMMDCCXLIV
3745 = MMMDCCXLV
3746 = MMMDCCXLVI
3747 = MMMDCCXLVII
3748 = MMMDCCXLVIII
3749 = MMMDCCXLIX
3750 = MMMDCCL
3751 = MMMDCCLI
3752 = MMMDCCLII
3753 = MMMDCCLIII
3754 = MMMDCCLIV
3755 = MMMDCCLV
3756 = MMMDCCLVI
3757 = MMMDCCLVII
3758 = MMMDCCLVIII
3759 = MMMDCCLIX
3760 = MMMDCCLX
3761 = MMMDCCLXI
3762 = MMMDCCLXII
3763 = MMMDCCLXIII
3764 = MMMDCCLXIV
3765 = MMMDCCLXV
3766 = MMMDCCLXVI
3767 = MMMDCCLXVII
3768 = MMMDCCLXVIII
3769 = MMMDCCLXIX
3770 = MMMDCCLXX
3771 = MMMDCCLXXI
3772 = MMMDCCLXXII
3773 = MMMDCCLXXIII
3774 = MMMDCCLXXIV
3775 = MMMDCCLXXV
3776 = MMMDCCLXXVI
3777 = MMMDCCLXXVII
3778 = MMMDCCLXXVIII
3779 = MMMDCCLXXIX
3780 = MMMDCCLXXX
3781 = MMMDCCLXXXI
3782 = MMMDCCLXXXII
3783 = MMMDCCLXXXIII
3784 = MMMDCCLXXXIV
3785 = MMMDCCLXXXV
3786 = MMMDCCLXXXVI
3787 = MMMDCCLXXXVII
3788 = MMMDCCLXXXVIII
3789 = MMMDCCLXXXIX
3790 = MMMDCCXC
3791 = MMMDCCXCI
3792 = MMMDCCXCII
3793 = MMMDCCXCIII
3794 = MMMDCCXCIV
3795 = MMMDCCXCV
3796 = MMMDCCXCVI
3797 = MMMDCCXCVII
3798 = MMMDCCXCVIII
3799 = MMMDCCXCIX
3800 = MMMDCCC
3801 = MMMDCCCI
3802 = MMMDCCCII
3803 = MMMDCCCIII
3804 = MMMDCCCIV
3805 = MMMDCCCV
3806 = MMMDCCCVI
3807 = MMMDCCCVII
3808 = MMMDCCCVIII
3809 = MMMDCCCIX
3810 = MMMDCCCX
3811 = MMMDCCCXI
3812 = MMMDCCCXII
3813 = MMMDCCCXIII
3814 = MMMDCCCXIV
3815 = MMMDCCCXV
3816 = MMMDCCCXVI
3817 = MMMDCCCXVII
3818 = MMMDCCCXVIII
3819 = MMMDCCCXIX
3820 = MMMDCCCXX
3821 = MMMDCCCXXI
3822 = MMMDCCCXXII
3823 = MMMDCCCXXIII
3824 = MMMDCCCXXIV
3825 = MMMDCCCXXV
3826 = MMMDCCCXXVI
3827 = MMMDCCCXXVII
3828 = MMMDCCCXXVIII
3829 = MMMDCCCXXIX
3830 = MMMDCCCXXX
3831 = MMMDCCCXXXI
3832 = MMMDCCCXXXII
3833 = MMMDCCCXXXIII
3834 = MMMDCCCXXXIV
3835 = MMMDCCCXXXV
3836 = MMMDCCCXXXVI
3837 = MMMDCCCXXXVII
3838 = MMMDCCCXXXVIII
3839 = MMMDCCCXXXIX
3840 = MMMDCCCXL
3841 = MMMDCCCXLI
3842 = MMMDCCCXLII
3843 = MMMDCCCXLIII
3844 = MMMDCCCXLIV
3845 = MMMDCCCXLV
3846 = MMMDCCCXLVI
3847 = MMMDCCCXLVII
3848 = MMMDCCCXLVIII
3849 = MMMDCCCXLIX
3850 = MMMDCCCL
3851 = MMMDCCCLI
3852 = MMMDCCCLII
3853 = MMMDCCCLIII
3854 = MMMDCCCLIV
3855 = MMMDCCCLV
3856 = MMMDCCCLVI
3857 = MMMDCCCLVII
3858 = MMMDCCCLVIII
3859 = MMMDCCCLIX
3860 = MMMDCCCLX
3861 = MMMDCCCLXI
3862 = MMMDCCCLXII
3863 = MMMDCCCLXIII
3864 = MMMDCCCLXIV
3865 = MMMDCCCLXV
3866 = MMMDCCCLXVI
3867 = MMMDCCCLXVII
3868 = MMMDCCCLXVIII
3869 = MMMDCCCLXIX
3870 = MMMDCCCLXX
3871 = MMMDCCCLXXI
3872 = MMMDCCCLXXII
3873 = MMMDCCCLXXIII
3874 = MMMDCCCLXXIV
3875 = MMMDCCCLXXV
3876 = MMMDCCCLXXVI
3877 = MMMDCCCLXXVII
3878 = MMMDCCCLXXVIII
3879 = MMMDCCCLXXIX
3880 = MMMDCCCLXXX
3881 = MMMDCCCLXXXI
3882 = MMMDCCCLXXXII
3883 = MMMDCCCLXXXIII
3884 = MMMDCCCLXXXIV
3885 = MMMDCCCLXXXV
3886 = MMMDCCCLXXXVI
3887 = MMMDCCCLXXXVII
3888 = MMMDCCCLXXXVIII
3889 = MMMDCCCLXXXIX
3890 = MMMDCCCXC
3891 = MMMDCCCXCI
3892 = MMMDCCCXCII
3893 = MMMDCCCXCIII
3894 = MMMDCCCXCIV
3895 = MMMDCCCXCV
3896 = MMMDCCCXCVI
3897 = MMMDCCCXCVII
3898 = MMMDCCCXCVIII
3899 = MMMDCCCXCIX
3900 = MMMCM
3901 = MMMCMI
3902 = MMMCMII
3903 = MMMCMIII
3904 = MMMCMIV
3905 = MMMCMV
3906 = MMMCMVI
3907 = MMMCMVII
3908 = MMMCMVIII
3909 = MMMCMIX
3910 = MMMCMX
3911 = MMMCMXI
3912 = MMMCMXII
3913 = MMMCMXIII
3914 = MMMCMXIV
3915 = MMMCMXV
3916 = MMMCMXVI
3917 = MMMCMXVII
3918 = MMMCMXVIII
3919 = MMMCMXIX
3920 = MMMCMXX
3921 = MMMCMXXI
3922 = MMMCMXXII
3923 = MMMCMXXIII
3924 = MMMCMXXIV
3925 = MMMCMXXV
3926 = MMMCMXXVI
3927 = MMMCMXXVII
3928 = MMMCMXXVIII
3929 = MMMCMXXIX
3930 = MMMCMXXX
3931 = MMMCMXXXI
3932 = MMMCMXXXII
3933 = MMMCMXXXIII
3934 = MMMCMXXXIV
3935 = MMMCMXXXV
3936 = MMMCMXXXVI
3937 = MMMCMXXXVII
3938 = MMMCMXXXVIII
3939 = MMMCMXXXIX
3940 = MMMCMXL
3941 = MMMCMXLI
3942 = MMMCMXLII
3943 = MMMCMXLIII
3944 = MMMCMXLIV
3945 = MMMCMXLV
3946 = MMMCMXLVI
3947 = MMMCMXLVII
3948 = MMMCMXLVIII
3949 = MMMCMXLIX
3950 = MMMCML
3951 = MMMCMLI
3952 = MMMCMLII
3953 = MMMCMLIII
3954 = MMMCMLIV
3955 = MMMCMLV
3956 = MMMCMLVI
3957 = MMMCMLVII
3958 = MMMCMLVIII
3959 = MMMCMLIX
3960 = MMMCMLX
3961 = MMMCMLXI
3962 = MMMCMLXII
3963 = MMMCMLXIII
3964 = MMMCMLXIV
3965 = MMMCMLXV
3966 = MMMCMLXVI
3967 = MMMCMLXVII
3968 = MMMCMLXVIII
3969 = MMMCMLXIX
3970 = MMMCMLXX
3971 = MMMCMLXXI
3972 = MMMCMLXXII
3973 = MMMCMLXXIII
3974 = MMMCMLXXIV
3975 = MMMCMLXXV
3976 = MMMCMLXXVI
3977 = MMMCMLXXVII
3978 = MMMCMLXXVIII
3979 = MMMCMLXXIX
3980 = MMMCMLXXX
3981 = MMMCMLXXXI
3982 = MMMCMLXXXII
3983 = MMMCMLXXXIII
3984 = MMMCMLXXXIV
3985 = MMMCMLXXXV
3986 = MMMCMLXXXVI
3987 = MMMCMLXXXVII
3988 = MMMCMLXXXVIII
3989 = MMMCMLXXXIX
3990 = MMMCMXC
3991 = MMMCMXCI
3992 = MMMCMXCII
3993 = MMMCMXCIII
3994 = MMMCMXCIV
3995 = MMMCMXCV
3996 = MMMCMXCVI
3997 = MMMCMXCVII
3998 = MMMCMXCVIII
3999 = MMMCMXCIX

Korn shell hack of the day

2010-10-07T20:30:00.002-04:00

or, "Scope creep and you, a typical example of the modern IT project"

Sometimes I find myself knee deep in a complicated shell script that probably would have been better off written in perl or Java. Today was one of those days. What started as a simple script I wrote for managing sftp traffic to a couple vendors has been transmogrified to handle calling Glub to do an ftps transfer (the "other" secure FTP) from a vendor, then delivering the files to an internal Windows share drive. So far so good, but feature bloat ended up straining my creativity to tackle each new problem, and ultimately saddled me with a workable solution that, while interesting, is sort of a stinker.

The connection to the Windows share was supposed to be via a mounted drive. I would copy the files to a Unix directory, and Unix would manage the SMB transfer transparently. This turned out to be unsupported by our data services group unless the Windows server in question was virtual. It was not. So suddenly I'm on the hook for adding SMB support to the process.

A quick search revealed the JCIFS library, which I was able to turn into a Java class that takes commandline inputs for destination server and path, and reads credentials from a config file. Just call "java ToShare" instead of Unix's "cp", and Bob's your uncle. Of course, the script has to grow a little bit to handle the extra config variables, where to find java, and what the classpath should be.

Second, the Windows guy was having problems automating unzipping the files before feeding them to his app. For whatever reason, the approach we settled on was to have my script unzip the files, and send him the artifacts AND the original .zip files. So the script needed to grow in complexity, managing unzipping and iterating through the unzipped artifacts, and the source archives, and sending each over my java SMB hack. Which looks like this:

# Simple log function. Echo the date and passed message to the logfile
logit(){
  echo "`date` $1" >> $LOGFILE
}

# If there's an error, call this, which sends a notification email and exits
error_handler() {
  echo "$1" | mailx -s"FTPS receive script failure" $ERROR_EMAIL_ADDRESS
  logit "$1"
  exit 1
}

# Error checker which run after most commands, if the return code from the previous command
# isn't 0, give the error message specified to error_handler.
check_error() {
  if [ $? -gt 0 ]
  then
    error_handler "$1"
  fi
}

# Find all the files we downloaded, and unzip them, sending output to the logfile
find $LOCAL_DIR/* -prune -name "$REMOTE_FILE_PATTERN" -exec unzip -d $LOCAL_DIR {} >> $LOGFILE \;
check_error "unzip failed"

# Output from unzip will contain either "inflating" or "extracting" for each file in the archive.
# Look for these messages in the log file, find the filename part, and iterate over them
for file in `grep -e inflating: -e extracting: $LOGFILE | awk '{print $2}'`
do
  # Run the SMB program to send the file to the Windows share...
  $SMB_CMDLINE ToShare $file $SMB_SERVER $SMB_PATH
  check_error "Failed to copy $file to $SMB_SERVER"
  # ...and then delete it. This is fine because the original zipped files are untouched.
  rm $file
  check_error "Failed to delete $file"
done

# Next, do the same thing for the zipped files themselves...
for file in `find $LOCAL_DIR/* -prune -name "$REMOTE_FILE_PATTERN"`
do
  $SMB_CMDLINE ToShare $file $SMB_SERVER $SMB_PATH
  check_error "Failed to copy $file to $SMB_SERVER"
  # ...except just move the files to an archive directory
  mv $file $LOCAL_ARCHIVE_DIR
check_error "Failed to archive $file"
done
logit "Files successfully copied to $SMB_SERVER, moving files on remote server to archive directory"

After adding this functionality, I was cursing my desire to do this in shell instead of writing a real program. But as these things go, the project's timeline was short, and starting over was out of the question. Plus, as I'm wont to do, I gave a lot of assurances that a file transfer script was a no-brainer before I had all the facts - one of the facts being that the vendor was using ftps, not sftp as advertised, the whole reason I chose this script template in the first place.

Third, the vendor requested that after downloading files, that they be moved to an archive directory on the vendor's ftps server. Normally it's polite to delete a file after you download it from a vendor, as it saves them space requirements, and can also let them know at a glance what files have been pulled. Moving a file to another directory is asked for rarely, but usually isn't a problem. For this process, however, multiple files would be available at once, all of which had timestamps in the filename instead of fixed names. A tolerable approach would have been to download and delete using mget and mdel, but there is no facility in standard ftp clients for batch renames on the remote server.

Had I started with perl, I could have played with named pipes and searching logfiles for filenames to build a set of rename commands to print to the pipe. Had I started with Java, I could have used the Glub bean and managed the ftps session on the fly, getting a file list and iterating over it with RETR and RNFR/RNTO commands. And there wasn't time to do either. And the Unix "expect" program wasn't installed, so I couldn't manage the ftps session that way. No, I was unfortunately going to have to do this in two sessions. Workable, but ugly, and it's generally considered bad mojo to log on to a server twice in the same process. But that's what I did.

Fortunately, Glub logs all the server RETR commands, giving me something simple to grep for with which to build a list:

# Build the multiple rename (mren) string. For each logfile line starting with "RETR",
# print out a corresponding line that says "rename (file) archive/(file)", save as $MREN
export MREN=`perl -lne 'if (/^RETR /){s!RETR (.+)!rename $1 $ENV{REMOTE_ARCHIVE_DIR}/$1!;print}' $LOGFILE`

# Log on to remote ftps server, execute $MREN lines
$JAVA -Dglub.user.dir=$HOME -Duser.dir=$FTPS -jar $FTPS/secureftp2.jar <<EOF
log $LOGFILE
open $FTPS_HOST $FTPS_PORT
user $FTPS_USER $FTPS_PASS
cd $REMOTE_DIR
$MREN
bye
EOF
check_error "ftps archive session failed"

logit "Session successful"

So eventually I'll be able to circle around and write this in a more sensible manner, or better yet, convince the vendor that they're better off if I just delete the files, and the Windows people that unzipping is really a breeze. The good news to all this madness is that I added about 10% to my commandline Unix bag of tricks, and you really can do a lot of neat stuff with shell scripts.

Picnic with the missus

2010-10-03T08:13:00.003-04:00

Liberty got this cool wicker picnic basket on eBay a while ago, and we decided to take it out for a spin yesterday. One of the better side effects of "bill week" (when your bills all come due at once, and your budget spreadsheet looks a little scary) is that you can find fun money savers that double as relationship builders.

Instead of spending $20 on a movie and snacks just to sit in the dark and be quiet, let's go out for a walk in the sunshine and talk to each other... for free. Instead of stopping for greasy fast food somewhere, or spending more at a better restaurant, let's cook up some food for lunch, and take it with us somewhere. In this case, "some food" was steak cut into strips and fried up with pepper, sweet Italian mini bread, cheddar cheese cut into slices, some green onion, and a refreshing carbonated beverage (the basket has a cool separate area for bottles), and "somewhere" was Highbanks park.

When we got there, we found a long trail that didn't seem to have a lot of people on it, and proceeded to hike around looking for unofficial exit points: Good places to hang out that are accessible, hidden from the trail, but without signs saying not to go there. What we found was here:

View Larger Map

Although the spot wasn't visible from the main trail (Dripping Rock, I believe), another trail frequented with dog walkers came close to it, and there was an occasional group of walkers coming near enough to see us, had they been paying attention to their surroundings. I think a couple people noticed us, but most people walked right by, oblivious.

At one point, a ranger came driving by in one of their little Jeeps, who was for all appearances looking for people hiding in the woods. He happened to turn his head the other way as he drove by - twice! Once on the way out from his station, once on the way back to it. Funny, but, I mean, come on dude! At any rate, we spread our blanket, ate our makeshift steak sandwiches, chatted, watched the clouds, and left the area as we found it - minus a few burrs, that is.

While hiking and rescuing the occasional woolly worm, we also people-watched. We had higher hopes for our fellow man there. Since we were in the woods, people should be healthier and less mainstream, no? "The Game" was on, so clearly the people at the park that day shouldn't be uber-consumer sports fans, and they should mostly be healthier and not couch potatoes. So one would think, but not the case. No matter how far we got from the main non-trail area, we would still hear the occasional yawp of joy as some sort of praiseworthy action from the game was reported on the radio. For some the exercise of walking up the trail's first hill was clearly the most punishment they had given their body in some time. There was also the occasional person walking on the trail while talking on their cellphone, forgivable, but lame. One of the families walking had an indifferent dad who busied himself with looking at trees or fields, making sure to keep himself a few feet away from his wife and kids. Why are you out with your family, exactly? If you don't like them, cut the cord now and lessen the pain on everyone. Don't put on the thin facade of just being stoic when your family can feel the vacuum where your love is supposed to be. Asshole. That part was the worst.

All was not lost, though. Most of the groups were clearly happy to be both together and out trekking through the woods. Most of the people were, indeed, healthy. There was this 50-something woman running with a practiced pace, listening to her iPod, and looking like she could confidently stave off attacks from local bears or mountain lions... I'm fairly certain we have neither, but still, when the fight goes down, I want granny on my side.

Lastly, there was a family whose mom or eldest daughter (I couldn't tell her age very well) was clearly recovering from cancer treatments, as she had the telltale wig, missing eyebrows, and extra lipstick, and was more fatigued than the rest of her group. But still out building up strength, building strong family bonds, and looking forward. When you hike the trail despite feeling bad, you're looking forward. When you let your family bring you to the park for the "fresh air" and just sit at a picnic table, you're waiting to die. She was looking forward, as was her family, who wasn't treating her as though she were fragile. That part was the best.

We had a lot of fun on the cheap. Despite the few stinkers, most of the people ranged from tolerable to downright enjoyable. And although next weekend I should have some actual disposable income, maybe we'll just bank it and do something free and outside instead.

Bezier Curves as Ellipses

2010-09-30T06:27:00.003-04:00

A couple weeks ago, I was exploring the source code for the Java runtime classes, trying to figure out exactly how Java draws a circle, and was surprised at what I found. A circle can be defined as an instance of the java.awt.geom.Ellipse2D class with equal width and height. Graphics2D attempts to draw the Ellipse2D shape by calling for its PathIterator. A PathIterator returns segments of the shape in the form of SEG_MOVETO, SEG_LINETO, SEG_QUADTO (quadratic Bezier curve), SEG_CUBICTO (cubic Bezier curve), or SEG_CLOSE. An Ellipse2D contains an initial MOVETO, four CUBICTO segments, and a final CLOSE.

I eventually got my head around what that meant and its implication: The standard 2D graphics library doesn't concern itself with center points and radii, or foci, or pi. In fact, it doesn't even render a real circle, but a very close approximation. It renders four cubic Bezier curves representing 90 degree arcs of the circle. I found this discovery strange at the time, but on reflection it made sense.

First, turning the radius and angle into Cartesian coordinates requires using sine and cosine functions. Java doesn't contain its own sine calculator or lookup table, it delegates to a native library. Second, once all the Bezier control points are established, no expensive division or square roots need to be done in order to calculate the curve. Only addition, subtraction, and multiplication. Third, while conic sections can all be represented by Bezier curves, the reverse is not true, so if you had to pick one, Bezier would be it. Lastly, applying affine transforms to curves is as easy as applying the transforms to the control points and redrawing. So basically these curves look the same to the naked eye as a circle, and are easier on the processor to render. Whether or not that's why the Java developers went that direction, I have no idea.

So, what's a Bezier curve, anyway?

A Quadratic Bezier curve is a distortion to a straight line with a single "control point" that has influence over it, acting like a sort of gravity well. The closer a point on the line would be to the control point, the more the curve is distorted from the line.

Plotting the curve is surprisingly simple. Start with a line between the start and control points, and another between the control and end points.

Next, pick a percentage, that we'll call "t". Plot a point t% between start and control, and another t% between control and end. Draw a line between these points. On this ancillary line, the point at t% gets added to the curve.

That's it. Repeat this for all possible "t"s, and you have your curve. Below is a simplified example, showing t at 25%, 50%, and 75%:

This shows the same curve at 5% iterations instead of in quarters, showing more detail of the curved shape:

A Cubic Bezier curve functions on the same basic principle, except there is an additional control point distorting the curve. Plotting them out is similar, but you have two ancillary lines instead of one, which you draw an... ancillarier? tertiary? line between, as illustrated here:

You can make fancier shapes with a cubic curve, such as moving one control point on the opposite side of the start/end line to make an s-shape:

Neat, but doesn't help us draw a circle. What does, however, is the equation for kappa, , which G. Adam Stanislav derives for us here. If the start and end points are on opposite corners of a square, and control points are on perpendicular lines, each kappa * side away from a termination point, a circular arc is drawn:

...which is the way Java does it. The equation for kappa evaluates to roughly .5522847498307933, which Java has as a static variable in the java.awt.geom.EllipseIterator class, to avoid needing to calculate a square root every time a circle is drawn.

public static final double CtrlVal = 0.5522847498307933;