The Life of a Mathematician

8:47

2008-03-31T08:47:00.003-06:00

After a ridiculous amount of time spent on it, I've got a solution to the last problem on the Linear Algebra test. It does not resemble the solution that seems to be described by the hint. I don't think I care at this point. What's frustrating is how simple the approach is that I ended up using, and the fact that I almost started with that approach, then got sidetracked by the hint.

Also, I added extra movie quotes to the ones that didn't get guessed yet.

6:32

2008-03-19T06:32:00.002-06:00

Two more days before I'm supposed to get a root canal, and my tooth has decided to start hurting again. My plans of catching up with differential equations yesterday evening were derailed by the need to use strong medication and then wait for it to start working. I can't even chew with the teeth on the other side without bothering it. I'll have to call the dentist later and see if this is to be expected, but I imagine so. He said we ought to do the root canal after a week, but that there wouldn't be problems if we did it within two weeks. Then they couldn't manage to schedule it sooner than three weeks later.

I like working in the extended reals. I was introduced to the concept a few years ago, but it still feels like doing something exciting and forbidden. I've told undergraduates that the derivative allows us to sort of get around not being able to divide by zero; it's like saying, "We can't divide by zero, but if we could, this is what the answer would be." However, the extended reals allow for it much more directly. You can call infinity a number, and you can divide by zero, and various other impossible things. You just have to put a few restrictions in to avoid paradoxes. I remember wondering in high school why division by zero had to be "undefined". If it's undefined, why can't we just define it? The answer was that if we defined it in the obvious way, we got problematic results. Turns out you can just forbid any action that would lead to those results.

21:29

2008-02-26T21:29:00.004-07:00

Okay, I found these on Qalmlea's blog (see Sporadic Maunderings in the list of links) and I've never done something like this here before and it sounds kind of fun. Basically how it works is I reproduce the rules, then I follow the rules, then if someone else sees it and likes it they do the same thing on their own blog.

Meme rules:
1. Pick 15 of your favourite movies.
2. Go to IMDb and find a quote from each movie.
3. Post them here for everyone to guess.
4. Fill in the film title once it's guessed.
5. NO GOOGLING/using IMDb search functions. Totally cheating, you dirty cheaters.

Slight modification: These aren't necessarily my favorite movies so much as movies I liked that I decided to include.

Identifications:

5. The Goonies
8. Aliens

1. "I am making out the report now. We haven't quite decided yet whether he committed suicide or died trying to escape."
"How extravagant you are, throwing away women like that. Some day they may be scarce."

2. "Ah, arrogance and stupidity all in the same package. How efficient of you."
"He was the best of us. They struck without provocation, there was no reason. Animals! Brutal! They deserve no mercy! Strike them down, follow them back to their base and kill all of them, all of them! No mercy!"

3. "Department of Commerce. She's a secretary. They have a man they call the Secretary, but he isn't at all. My mother's a real secretary."
"He was very nice about it, but he made me feel like a third-class witch doctor."

4. "Maybe it's better not to be the best. Then you can lose and it's OK."
"You've lost, you just don't know it yet."

5. "Everything. OK! I'll talk! In third grade, I cheated on my history exam. In fourth grade, I stole my uncle Max's toupee and I glued it on my face when I was Moses in my Hebrew School play. In fifth grade, I knocked my sister Edie down the stairs and I blamed it on the dog... When my mom sent me to the summer camp for fat kids and then they served lunch I got nuts and I pigged out and they kicked me out... But the worst thing I ever done - I mixed a pot of fake puke at home and then I went to this movie theater, hid the puke in my jacket, climbed up to the balcony and then, t-t-then, I made a noise like this: hua-hua-hua-huaaaaaaa - and then I dumped it over the side, all over the people in the audience. And then, this was horrible, all the people started getting sick and throwing up all over each other. I never felt so bad in my entire life."

6. "It's not that hard. You just call her up and say, 'Hello, I'm a lying grease monkey.'"
"'New Jersey: Leader in Intergalactic Rocket Exploration.' How's that sound for a license plate?"

7. "Who is this jerk? And who told him he could turn off my music?"
"Don't tell me you've never seen the moon before."

8. "I say we take off and nuke the entire site from orbit. It's the only way to be sure."

9. "It smells like puke from a mule been 'ruminating on asparagus for two weeks."
"I'm depending on you. It should be no labor to be nice to your neighbor."

10. "We have the magic rocks. They will keep us safe."
"Why have we not heard of these rocks before?"

11. "But captain, to obey - just like that - for obedience's sake... without questioning... That's something only people like you do."
"Hi! Are you a fairy?"

12. "You're more advanced than a cockroach, have you ever tried explaining yourself to one of them?"
"In the end it all came down to just one simple question. Which was more important - having proof, or being alive? Trust me. I turned away years ago, and I've never looked back."

13. "Yeah, he's fast! But he won't go any faster. He's a gut runner, digs deep! But a short sprint is run on nerves. It's tailor-made for neurotics."
"My arrogance, sir, extends just as far as my conscience demands."

14. "Good heavens, woman! This is a war, not a garden party!"
"I can shoot straight, if I don't have to shoot too far."

15. "I can't ask him what he's doing. I'm supposed to tell him what he's doing. I ask him what he's doing and I'm gonna look like an idiot."
"Buddy, I think you been spending too much time inhaling them cleaning products."

21:22

2007-12-05T21:22:00.000-07:00

3*7:2*11
2*1061

This is not an update about life. Sue me or something.

Any prime number greater than 3 must be of the form 6n + 1 or 6n - 1. This kind of shows why twin primes are a natural concept. Furthermore, twin prime pairs greater than 25 must be of the form 6n - 1 and 6n + 1 with n not divisible by 3. I haven't worked out what restrictions occur when 7 is thrown into the mix after 49.

12:04

2007-10-15T12:04:00.000-06:00

2*2*3:2*2
2*2*7*43

There's a hole in my counting argument, dear Liza, dear Liza...

6:18

2007-10-12T06:18:00.000-06:00

2*3:2*3*3
2*3*103

It turns out the mantis is female. I feel pretty confident in stating this, since she laid eggs. I thought I remembered the one I had in high school laying them every two or three weeks, but now I realize even if that is the case they don't do it all year round. She started looking pregnant around the same time as she ate a bunch of crickets, so that threw me off. Also, I noticed that she was acting sluggish, but thought maybe it was just from having overeaten. I think her name is Matilda.

I didn't blog about this at the time, but I have a solution, of sorts, to the topology/combinatorics problem, although some of the results found on the way there are probably more significant. Turns out there's good news and bad news about my approach. The good news is quite a bit of it could be unique. The bad news is this is because it's in an area of study generally considered to be uninteresting. Dr. Kratz wants to see it anyway, as soon as I've got it all written up nicely.

I've moved the comics links over to the Stickromancer blog. Also, I've found a new comic called The Dreamland Chronicles. It's the first thing I've seen in a while that I think rivals Schlock Mercenary in quality.

11:42

2007-10-04T11:42:00.000-06:00

11:2*3*7
2*571

So I was solving a system of linear equations using an appended matrix, and I didn't want to take up the whole chalkboard with a series of matrices so I was just erasing entries and rewriting them as I went about the process of diagonalizing and normalizing it. You all relate, I'm sure. At one point I had just erased and rewritten a couple of entries and was unsure whether I'd gotten one of them right, so I wanted to see what it had been before I erased it. I felt my left hand automatically moving to press control-z. Unfortunately, the chalkboard does not support that feature. The secretary in the math department office says this does not make me crazy. She sits in front of a computer all day, so she may be biased.

9:18

2007-10-02T09:18:00.000-06:00

3*3 : 2*3*3
2*3*3*3*17

I'm posting something, just to break the monotony of not posting and try to get back in the habit. I have class in ten minutes. Applied math homework is taking too much effort.

11:06

2007-09-06T11:06:00.000-06:00

11:2*3
2*7*79

New approach to the topology/combinatorics problem:

Suppose we have two sets: (x1, x2, ... , xm) and (y1, y2, ... , yn) where m, n are positive integers, and we have a collection P of ordered pairs of the form (xj, yk) where 1 <= j <= m, 1 <= k <=n.

There are m*n possible ordered pairs of this form, and therefore 2^(m*n) possible collections. But suppose we add the following restriction: For any k between 1 and n, there exists j between 1 and m such that (xj, yk) is an element of P. In other words, every element of the second set has to be used in at least one ordered pair.

How many possible collections are there that satisfy this stipulation?

20:56

2007-09-01T20:56:00.000-06:00

2*2*5:2*2*2*7
2*2*2*257

This evening I caught a praying mantis. Now I must feed it things.

14:49

2007-08-29T14:50:00.000-06:00

2*7:7*7
3*3*7*23

Today they had the big white tent set up with all the campus organizations. I spent a couple of hours helping hand out stuff at the Crossroads Christian Fellowship table, then taking boxes back to the church office. I looked for the math club table and didn't see it if it was there.

I broke my 4x4x4 Rubic's Cube. One of the face pieces snapped, and without it the rest won't hold together. I'm fairly sure it wasn't built as well as the smaller one, or maybe the larger size is harder to make sturdy, because I definitely didn't use it as much.

Lots of things going on Friday. There's a math department get-together, followed by a movie and game night with the Crossroads crowd. I probably won't make it to Randy's, but it's fantasy football draft night there anyway.

10:57

2007-08-28T11:07:00.001-06:00

7*151

The reports of my abduction by illegal aliens were slightly exaggerated.

There have been some changes to the sidebar; mostly I've removed inactive blogs and added some new comics. Making my own comic strip has increased my interest in looking at other people's.

I find it entertaining the way one can cause a math professor to break stride in his lecture simply by pointing out some real-world condition that relates to the problem. Today in differential equations we were looking at a simple population growth model. At some point we had the equation ax(x-1) = 0, and came to the conclusion that x = 0 or x = 1. The professor asked what we were assuming for this conclusion, and the answer was that a <> 0. I pointed out that this would imply a static population, which doesn't happen. It took him a minute to figure out what I was saying, then he replied with something like, "Oh, that's true for populations in real life, but we're considering an ideal situation." These ideal creatures, which can sometimes have constant populations, are presumably identical and spherical.

21:27

2007-05-07T21:26:00.000-06:00

3 * 709

On Saturday I visited the local museum. I think the last time I was there was over ten years ago. Some things are exactly as I remember them. For instance, there are lots of arrowheads and other Indian artifacts. Some things are quite different. They didn't used to have live animals (an iguana, a large snake, and poison dart frogs) and they didn't used to have fossils, even in replica form. The most impressive display hasn't been completed yet, but it's going to be a complete replica of a wooly mammoth skeleton. Right now there's just the skull and a leg.

Saturday evening I went with my parents to the last showing of Macbeth in the CSI fine arts building. It was a decent rendition; my biggest regret was that they didn't have a better actor playing the heir to the throne. He enunciated well, but gave no appropriate inflection. This showed up strongly when he had dialogue with Macduff, who was a very good actor. The witches were quite skilled at their evil cackling.

I've started a new blog for my comic strip. I'd been posting it on a private forum, but this way it will be more accessible. The address is www.stickromancer.blogspot.com, which I will add to the links on this page. I guess this would be a good time to make clear that "stickromancer" is a pun on the word "necromancer" and the fact that I'm using stick figures. It is not a reference to someone who woos sticks.

15:05

2007-04-23T15:04:00.000-06:00

5*7*43

I just made a post about a strange dream on my other blog that you probably thought I had abandoned.

17:05

2007-04-12T17:15:00.000-06:00

5*11*31

I seem to be having difficulty keeping this updated.

I quite the Mandarin House job because there aren't enough deliveries during the summer to make it worthwhile. In the meantime, the weather has failed to become sufficiently warm to increase business at my day job to the point where I can work more hours. I am tutoring a couple of high school students in geometry on Fridays, though.

Since the introduction of the labeling feature, I always have an urge to write a post about going on vacation in the fall and riding scooters. I've never done this, not even in Boston.

I want to figure out how Sudoku puzzles are constructed. Enough numbers have to be left so that there is only one possible solution.

13:55

2007-03-09T13:54:00.000-07:00

Er, make that 4 hours last night. For some reason it felt like Friday when I was posting.

I'm rather disappointed that no one has suddenly solved the graph problem from a few posts back. I thought if I put it on the Internet then, you know, millions of people would see it and someone would be sure to solve it.

15:47

2007-03-08T15:55:00.000-07:00

I had to drive to Boise today to pick up a pallet of boxes. I don't actually know what was in the boxes, because I clocked out as soon as I got back. The drive was long and the plastic wrap on the pallet came loose a couple of times and I had to stop and resecure it. Now I get to go drive for 4.5 more hours tonight. With breaks of course. And probably not at all for the last hour.

13:53

2007-03-05T13:59:00.000-07:00

I had a paint delivery today that was rather difficult to locate. The directions said to go south on 2500 East until I reached 3500 North, then turn right and drive west until I saw a house under construction on the right side of the road. So, I went south on 2500 E, and turned right when I got to the road labeled 3500 N. That ought to have been the correct road. But it quickly turned into a narrow, winding, dirt track with steep embankments on either side, and the only house anywhere near the road was on the left side with no way to get to it. It turns out there are two roads labeled 3500 N on that mile. The one I wanted was a bit further south and becomes a dead end when it hits 2500 E. Couldn't they have labeled the dirt track 3502 N or something?

16:00

2007-02-22T15:58:00.000-07:00

I've reduced the finite topologies problem to a problem of graph theory. On a given finite number of points, how many directed graphs can be drawn such that:

a) All the points are mutually connected.
b) Any two points are connected by at most one arrow.
c) Given three points X, Y and Z, if X points to Y and Y points to Z, then X points to Z.

It's been warmer outside recently and I decided to walk to the library today. Now I have to walk back.

14:25

2007-02-21T14:22:00.000-07:00

I'm not going to waste time explaining about my lack of posting.

I went along with Justin on the Hailey delivery today (about 3.5 hours, round trip). Currently this is done once a week, but during the summer it will be twice a week, and I'll probably be taking it a lot of the time. It's mostly a long, flat stretch with lots of sagebrush.

Sunday was the Chinese New Year. It's the Year of the Pig. My boss was very happy that day, and passed out little red "lucky envelopes" to all the employees, each containing two dollars.

The men's Bible study has been rescheduled to 6:30 instead of 7:00 on Thursday mornings, which means it is early enough that I can go to it now. My dad has been going also.

I've got four minutes still but that's probably all I have to type write now.

14:58

2007-01-17T14:57:00.000-07:00

I have bookshelves now. With books on them, even.

14:59

2007-01-06T15:00:00.000-07:00

I have a kitchen table and two chairs now. This improves the apartment significantly.

This week was very slow for deliveries through Wednesday, but last night and the night before were busy. Last night I had a delivery a long distance away that got called in about ten minutes before closing, so I got off a bit later than usual.

I worked a five hour shift today at the paint store, which is to say from open to close with the winter hours. It was dead for the first hour, then we got one customer who needed a quart of something (although he asked for a pint -- it comes in pints?) and a roll of masking tape. Then about an hour after that everyone came in at once and we were busy for a while. Just before close (de ja vu) I had to take a delivery of 2 gallons to a job site.

16:22

2007-01-03T16:21:00.000-07:00

All my boxes are unpacked, except the ones with books. I still have a lot to organize and put away, and I also need some basic furniture, like chairs. Tomorrow is my day off this week for the daytime job.

22:21

2006-12-31T22:19:00.000-07:00

This is an update, then.

I have two jobs now. During the day I work at a paint store, and in the evenings I'm a delivery driver for Mandarin House. I also have a car now. It's a 1995 Dodge Intrepid. I also have an apartment now. It's got two bedrooms and I'm looking for a roommate.

Tonight was a slow delivery night. Jack thought it would be very busy so he scheduled all three drivers. I would have been somewhat busy for a short time with two. With three it was very laid back. Not a good tip night. I did get to leave forty minutes early.

It was weird to see the new cook chopping vegetables. It's weird to see a white guy doing anything on that side of the kitchen. Actually, it's weird to see a white guy who's not Russian or Bosnian anywhere in the kitchen. I used to be the only one.

I don't go back to Kelly-Moore until Tuesday. So it's a three-day weekend for that job. Business is very slow there because it's winter, but we've had plenty to do rearranging the store.

I'd be hanging out with the family instead of typing this, but they're all playing poker, and I didn't get off work soon enough to join in.

Speaking of poker, it's been a long time since I've seen a Next Generation episode.

13:14

2006-11-11T13:20:00.000-07:00

This won't be much of a post, but it could be a while before I'm ready to post much else. I am back in Idaho, I've got a cold that won't go away, I'm placing applications to try to get a job, I've been a substitute math teacher twice, and I'm looking for a car.

11:25

2006-10-23T12:30:00.000-06:00

I made the trek to The River Academy this morning to say goodbye there. The bike ride was darker and colder than the last time I did it, but a pair of gloves made a tremendous difference. When I first walked out, the beauty of the night sky hit me with an almost physical force. I don't know why it came across so strongly; I've seen the stars recently. If I were more of a poet, I would write a hymn of praise to the Creator of Orion.

I decided to get off the bus before the station for once, since this could save me a few minutes in terms of when I started pedalling, and involved trading an uphill block for a level one. Unfortunately, I forgot which was the correct stop and ended up trading the uphill block for several level ones. I think I broke even and got to the school about the same time as I would have leaving from the station.

Since it was Monday, I was there for the weekly assembly. Afterwards, I talked to the precalc class for a few minutes, telling them where I was going and why, and taking the opportunity to say good things about their teacher behind his back since he was out of town today. I had spoken to all the faculty I knew before school started, so after taking my leave of the class I headed back to the bus station and was able to catch the 9:15.

I've got more than half my boxes packed, and should be able to ship some of them today since there will be too many for a single load.

21:20

2006-10-20T22:26:00.000-06:00

I didn't get the job, so I'll have to try and find a different one as quickly as I can. I had planned on moving whether I got the job or not, but not knowing what I'll be doing when I get there is decidedly less pleasant.

23:00

2006-10-19T00:05:00.000-06:00

I have definite travel plans now. Next Wednesday I will travel cross-state on the bus, and spend the night with Joel and Christie. Then Thursday I will fly to Boise, where my mom and sister will pick me up.

I still don't know if I'll get the job I've applied to.

16:40

2006-10-13T17:46:00.000-06:00

I have applied for a teaching job back in Idaho. If I get it, I'll be moving very soon. Meanwhile, work progresses on the Level 2 solutions manual.

16:12

2006-09-28T17:18:00.000-06:00

The abandonment of this blog is temporary. Really.

My internship is coming to an end, and I'm seriously thinking about going back to school.

In other news, suppose the Fibonacci rabbits had a fixed, finite lifespan? Suppose, for instance, that they spent one month as babies, three months as reproducing adults, and one month as old, non-reproducing rabbits before dying. The recursive formula ends up being more complex than I would have thought:

f(n) = f(n-1) + f(n-2) - 2*f(n-5) + f(n-6) + f(n-7)

8:14

2006-08-25T09:13:00.000-06:00

I've spent the past week grading placement tests, waiting for more placement tests to come in so I can grade them, trying to obtain definitive instructions for the grading system, and organizing all the data into a spreadsheet. Also, I had to break up the 10 files containing the solutions manual into 77 files. Now those 77 files all have to be broken into sections within each file, and each section needs a unique header. I've already done that for the first two chapters, but most of that job will be for early next week.

Meanwhile, the Ebys are having more houseguests this weekend than they have guest rooms to support, and the solution they have arrived at is to let me stay at Rivendell (one of the cabins they rent) for the weekend. This means I'll be without web access, so don't look for me online for a few days.

12:27

2006-08-17T13:31:00.000-06:00

I finished the solutions manual about an hour and a half ago.

9:38

2006-08-15T10:41:00.000-06:00

When constructing a regular polyhedron out of paper, one generally starts by drawing connected regular polygons, such that when they are cut out and folded on the common edges, they will become the faces of the solid. This process leads to a question. Assuming the polyhedron is made from a single piece of paper, how many different ways are there to draw the polygons? It turns out this is equivalent to the question of how many trees can be drawn on the dual polyhedron, where the vertices and edges of the trees are vertices and edges of the solid, and such that all the vertices are used.

20:11

2006-07-27T20:58:00.000-06:00

Last weekend my dad was in the area visiting his brother, so he came and visited me as well. He got here on Saturday afternoon and left early Monday morning. It was really good to see him, and I was glad he was here when he could visit my church. On Monday evening we went to the same Thai place that I went to with Amy (we found that #32 and #34 are both good) and Sunday evening we went to a German place that Dad picked out because he walked by and smelled the sauerkraut. In addition to sauerkraut and sausages they had live accordion music. On Sunday afternoon, once it cooled off a little (it had been over 100 degrees) we took a scenic drive that was recommended to us, turning around when the paved road gave out since we were in a rental car.

19:41

2006-07-26T20:32:00.000-06:00

It's been nearly a month so I should probably type something here. Mostly what I've been doing is working, and there hasn't really been any math that I've felt like blogging about, so it take too much to do an update.

The week of Independence Day I did in fact go to visit my friend Joel. I hadn't seen him in about five years, and I had never met his wife, Christie.

I got down there on Saturday evening. Sunday morning I went to church with them. After church we packed our lunch and drove to go meet his family at a lake in Idaho. We spent part of the afternoon driving around the lake in a boat, then had dinner with his family back at their camper. At some point in the conversation Joel tried to tell me that he loved logic proofs but hated math, so I had to explain to him that once you get past differential equations, proofs are what math is all about. He was rather surprised.

Monday night they invited some college students over to play board games. We played a card-game called "The Great Dalmudy," and another a card game called "Bang!" which is a more complicated variation of "Mafia" with an old-west shootout theme. I was "Willy the Kid," who has the special ability of being able to shoot his gun as many times as he wants on one turn (provided he's got the cards for it). I was also a Deputy, which meant my goal in the game was to support my local Sherriff. I did this by shooting at anyone the Sherriff shot at, and also by shooting at people I believed to be Outlaws who the Sherriff might not have shot at, and also by shooting whatever other random people were standing between me and the Outlaws. I did not, however, shoot the Sherriff. Except with the gatling gun, which hits everyone. We also played a very complicated game called "Shadows Over Camelot," in which the players assume the roles of various Knights of the Round Table, and work together to defeat the evil gameboard. You are required to address one another by proper titles, and can discuss game strategy, but only from an in-character perspective. For instance, you don't say, "I have army cards numbered 1 through 4, but I'm missing number 5," but rather, "I can aid Arthur in the campaign against the Picts, if he can provide the very strongest troops to finish the battle."

On Tuesday we went to one of the few counties (or possibly the only county) in Washington where fireworks are still legal. Some of the college students made dry-ice bombs, which we found out later are illegal even there. During the fireworks displays there was a huge thunderstorm going on with sheet lightning, which was much more impressive than the fierworks. Earlier in the afternoon, Joel was attacked by some boys with water guns, to which he responded by hooking up a hose and soaking one of them. He then suggested we move inside before it occurred to them that the hose could be used on him as well. While inside, we played a game called Politics, which is a bit like Life, only you pursue a political career. I was elected president twice, but in my second term I got impeached and removed from office. I don't know what the charges were, but I'm sure I was innocent.

Joel and Christie help out with their church's youth group, so on Wednesday night I sat in on that. On the way there Christie's car broke down and we had to push it across a busy intersection. It turned out the problem was a faulty heat gauge; it had crossed the red line for no good reason and a failsafe mechanism shut the vehicle down. It was nice that she had a larger passenger when it happened.

Wednesday and Thursday they both were at work during the day, so I just hung out at the apartment. I had brought the pre-algebra book with me so I was able to work on that. My bus left Friday morning.

20:42

2006-06-28T21:33:00.000-06:00

Earlier this week, Qalmlea (see the Sporadic Maunderings blog in the links list) took the long way while traversing to Oregon and visited me. As she mentioned on her blog, we went to a Thai restaurant, and the food was very good. It is always nice to meet an old friend again. I've relocated three times since finishing high school, and it seems like with each move it is harder to establish new connections when I know I'm probably going to have to sever them again. I try to keep in touch with people, but it doesn't always happen.

Monday evening and yesterday morning we had houseguests here. "We" at that time meant just myself, Mr. Eby, and Nala (the dog) because Mrs. Eby was still in Canada. This family that visited has ten children. The oldest is in college and the youngest is barely out of diapers. They said that they've decided ten is enough, and this is the first time the youngest has been that old.

Next week I'm visiting a friend from college who I haven't seen in about five years. I leave on Saturday and come back after the 4th on whatever day that week works out the best; the bus tickets are not date-sensitive.

Since I'm not likely to blog during that time, I'll post something patriotic right now:

Oh say, can you see by the dawn's early light
What so proudly we hailed at the twilight's last gleaming?
Who's broad stripes and bright stars through the perilous fight
O'er the ramparts we watched were so gallantly streaming!
And the rockets' red glare, the bombs bursting in air,
Gave proof through the night that our flag was still there.
Oh say, does that star-spangled banner yet wave
O'er the land of the free and the home of the brave?

On the shore, dimly seen through the mists of the deep,
Where the foe's haughty host in dread silence reposes,
What is that which the breeze, o'er the towering steep,
As it fitfully blows, half conceals, half discloses?
Now it catches the gleam of the morning's first beam,
In full glory reflected now shines in the stream:
'Tis the star-spangled banner! Oh long may it wave
O'er the land of the free and the home of the brave!

And where is that band who so vauntingly swore
That the havoc of war and the battle's confusion,
A home and a country should leave us no more!
Their blood has washed out their foul footsteps' pollution.
No refuge could save the hireling and slave
From the terror of flight, or the gloom of the grave:
And the star-spangled banner in triumph doth wave
O'er the land of the free and the home of the brave!

Oh! thus be it ever, when freemen shall stand
Between their loved home and the war's desolation!
Blest with victory and peace, may the heav'n rescued land
Praise the Power that hath made and preserved us a nation.
Then conquer we must, when our cause it is just,
And this be our motto: "In God is our trust."
And the star-spangled banner in triumph shall wave
O'er the land of the free and the home of the brave!

17:18

2006-06-21T18:12:00.000-06:00

I've added some links to the sidebar to non-blog websites run by people I know. If I know you and you have a website that I didn't list, tell me and maybe I'll list it.

The Turnbull family goes to my church here, and Matt Turnbull leads the Tuesday evening Bible study that I attend. Speaking of which, I forgot to go last night because it was about 21:30 before I remembered it was Tuesday. The website is about his wife's battle with cancer.

Wolff's Lair is the website of BlackWolff, who's blog is in the blog list. It's basically just a links page with three links. One link goes to a private forum that you already know about if you're a member, one takes you to his blog, and one goes to an alphabetical listing of his books, which is alarmingly long.

Visual Basic Thunder is run by a friend of mine from highschool. It's of particular interest if you are a programmer, particularly if you use VB 6.

22:22

2006-06-20T23:25:00.000-06:00

My lack of posting was due to allergies followed by schedule upheaval. Before the allergies, my friends John and Brandon visited me. They got here on a Tuesday evening and left on the following Thursday morning. Tuesday evening they went to Bible study with me, and afterwards we played my board game. The board game is no longer called "Wizards and Lizards," because I found some smaller rubber creatures at a toy store. They are mostly sea creatures, but that's okay. They fit on the tiles. They liked the game well enough to want to play it again on Wednesday night. We played cooperative and won both times, but the second time we found out afterwards that the Level 1 Flier card had been left out of the deck, which went a long way towards explaining why the flier didn't come attack us. Incidentally, that particular flier now looks like a blue pigeon.

Before that, we made an abortive attempt at hiking -- John got worn out quicker than he thought he would. That might have been when I inhaled whatever I was allergic to. We toured the town and did touristy sorts of things, including taking a tour of the local candy factory. It was really good to see them both again; TMC seems like it was ages ago now.

In other news, classes are out for the summer so it's just me and the solutions manual, which I hope to finish this month. Actually, for this week, it's just me, the solutions manual and the doggy. The Ebys had to go on an unexpected trip to Canada because Mrs. Eby's father died in the operating room on Friday morning. So far everything's gone well here, aside from the FedEx guy not showing up to deliver the equipment we're going to need when they start filming math lectures next week.

The other day while riding home I saw a dead deer on the side of the road. In fact, I had to swerve into the main traffic lane to get around it. A couple of days later, it had been moved off the road, but was still dead.

14:33

2006-05-27T15:32:00.000-06:00

Yesterday I got a package in the mail from my family with birthday presents. They sent me two books: Great Expectations by Charles Dickens, which I've never read, and The Three Musketeers by Alexandre Dumas, of which I've only read a very abridged version, along with watching various movie renditions, plus the Wishbone episode. They also sent me a photo album, filled with, um, photos. A few are ones I took at summer camp and stuff, but most are various family pictures. I am very pleased to have them, as I don't often take a lot of photos myself.

The other package that arrived yesterday contained a copy of Geometer's Sketchpad, which will allow me to go back and fill in all the graphs I had to skip over in the solutions I'm writing. One thing Adobe Illustrator does not do is graph equations.

22:22

2006-05-24T23:23:00.000-06:00

Well, I've got a system for counting the number of topologies on a given finite set of points that is much faster than listing them all, but it's still a long way from being a formula. However, it looks like it might eventually turn into a recursive formula. The trouble is that the recursion could be nested any number of levels deep.

23:24

2006-05-24T00:27:00.000-06:00

Today was my birthday, which makes me think of last year when I ended up helping Mike with algebra homework on that day, then later played Star Wars: Epic Duels with Abe, Greg and Kyle after Mike told them it was my birthday and I was by myself. And, this line of thinking is going to make me homesick so we'll move on to another.

Class this morning was talking about the final for the first few minutes, then the rest of the lecture was a biographical sketch of Euler. Quite interesting. I didn't remember that he was contemporary to Goldbach and mentored by Gauss. Then again, I have a poor memory for historical details in general. Next Tuesday he plans to answer any study questions they have, then prove that e^(i*pi) + 1 = 0.

After class we did the last round of placement testing (until this fall) with the homeschoolers. Just two students this time, a Level 2 and a Level 3. The boy taking the Level 2 test also had a birthday today. He turned 14. It also looks like he did well on the test, based on a quick look-over. I'll actually grade them in the morning.

While they were taking the test I started writing up more formally some thoughts I'd had about a problem some of us attempted when we were taking combinatorics. The problem itself comes from point-set topology. Given a finite set of n points, how many topologies are there on the set (assuming the points are distinguishable)? I realized it had been a while since I'd written up a technical proof, but it came back pretty quickly. I haven't gotten as far as trying to do any counting yet, but I've got what might be a good system for describing the topologies.

17:03

2006-05-21T18:04:00.000-06:00

On Friday I got a haircut. The barber shop also sells antiques and art. The guy that owns it does photography along with a little bit of painting. He used to be an engineer, and his favorite subjects are engineering and motorcycles. He was showing me a new technique they have for prints: There's a printer that actually puts paint onto canvas, so that the finished product looks like a painting. In a way I guess it is a painting, but it's done by machine. He showed me an example of the canvas print next to the photograph it was based on; the print looks a lot better because of the texture and depth.

Yesterday I helped move a large pile of broken drywall into a trailer to be hauled off. I was the wheelbarrow operator. It took about three hours. It's been hot recently, but we had cloud cover for a lot of that time.

Last night we had dinner with Mr. Nickel -- and his wife, who is finally back in town after being gone for about 4 months. We played Bocce Ball in the backyard. It's sort of a cross between croquet, bowling and horseshoes. One of the families had a ten-year-old named Nathaniel who was very enthusiastic about the game.

5:48

2006-05-16T06:52:00.000-06:00

Okay, I've found a way to become alert sooner than 6:00, while having technically slept the previous night. Can't say I care for it. The trick is to have a headache that starts in as soon as I lie down, and continues despite the fact that I fall asleep almost immediately, so that I continue to have the headache even while dreaming, which makes the dreams restless and frenetic, then sleep continuously until 5:00, wake up, walk into the restroom, and have the headache dissipate almost entirely as soon as I stand up. The contrast, combined with what seems like a reasonable fear that the headache might return if I lie down again, is sufficient to wake me up entirely. The restless and frenetic dream is on my other blog.

19:05

2006-05-14T20:01:00.000-06:00

On Friday, when I walked into the room before the first class with the homeschoolers, the teacher handed me a paper with a problem on it. It was the extra credit problem from the test that the algebra class (second hour) had just done, and he hadn't had time to find the solution for when they asked about it. Here's the problem:

The roots of a quadratic equation are 1 + sqrt(5) and 1 - sqrt(5). Find the equation.

There's a more difficult way to do it that finds an infinite family of solutions, and an easier way that finds just one solution. I demonstrated the more difficult way to the class, because that's what I thought of, but then a few minutes afterwards the easier method occurred to me so I showed them that as well.

23:40

2006-05-10T00:39:00.000-06:00

My brain absolutely refuses to function before 6:00 in the morning. Having had enough sleep helps once 6:00 arrives, but before that it just means I'm well-rested and unable to process information. The only exception to this rule is if I stay awake all night. In that case, my reasoning ability starts a process of exponential decay, beginning at 22:00 with a half-life of 90 minutes, but leveling out at around 2:30 when it reaches 25%. It'll hover there for the rest of the night, and then increase again as high as 70%, maybe even 80%, when I tap into emergency energy reserves at dawn. This spike lasts until sometime between 9 and 11, at which point my body insists on a complete shutdown for maintenance and repairs. All of this is assuming there is no caffeine involved.

No, I haven't had any reason to pull an all-nighter in this job, but I do have a reason for trying to wake up and start functioning at 5:30 on Tuesday mornings. I've gotten as far as the "wake up" part. My last roommate has a quote on record of me saying, "righteousness begins at 6 am". I believe this was in response to his request that I define what I meant by an "ungodly hour".

On the bus this morning I met a kid who is in high school, but is also taking Calculus 3 at a local junior college. Furthermore, it sounds like he's doing well and enjoying it. He thought that my job sounded like fun.

Almost no one showed up to Bible study tonight; just me, the guy whose house it's at (and not his wife since she's out of town), they guy who leads the study, and one of his daughters. As a result, it ended up being just a prayer meeting and shorter than usual.

I've been thinking about the Rubic's Cube, viewed as a group on six generators. Rather hard to come up with a complete list of relations.

I finished reading War and Peace by Leo Tolstoy, and The Jericho Sanction by Oliver North. I'm now starting over in my abridged version of The Journals of Captain Cook (from Penguin Classics). One interesting log entry from before the main voyage started:

"Wednesday 14th. Winds Easterly. First part fine clear weather, remainder Clowdy with squalls from the land attended with showers of rain. In the night the bend of the Hawsers of the stream Anchor slip'd, owing to the carelesness of the person who made it fast. In the morning hove up the Anchor in the Boat and carried it out to the Southward, in heaving the Anchor out of the Boat Mr Weir Masters mate was carried over board by the Buoy-rope and to the bottom with the anchor. Hove up the anchor by the Ship as soon as possible and found his body intangled in the Buoy-rope. Moor'd the ship with the two Bowers in 22 fathom water, the Loo Rock W and the Brazen head E Saild his Majestys ship Rose. The Boats imploy'd carrying the casks ashore for Wine and the caulkers caulking the Ships sides."

13:46

2006-05-07T14:44:00.000-06:00

It sprinkled a little when I was riding to church this morning and also on the way back, but already the clouds look like they might be moving on. It's been pretty hot recently.

I found out that the kids I was tutoring are pretty much done with math for the summer, so I don't have that job now. Maybe something else will turn up.

17:12

2006-05-06T18:12:00.000-06:00

I've started a new blog for recording my dreams. It's linked at the bottom of the blog list to the left. Also, Sudoku puzzles rated at five stars of difficulty are challenging.

11:54

2006-05-06T00:55:00.000-06:00

I haven't posted in a while, mostly because I've been too tired to compose a post when I've had time, or too busy catching up with other things when I've not been tired. But there really hasn't been that much going on. I write solutions, I sit in on classes, I attend church and Bible study, and I tutor. The bike ride has gotten easier so that it doesn't wear me out anymore, even in the coming back direction, which is slightly uphill and usually against the wind.

Recently we've been giving placement tests to a group of homeschoolers to assess what classes they'll be ready to take this fall. There's a local "homeschool co-op" group that meets every week and has once-a-week lectures in certain subjects. I helped administer the tests and then graded them; the results were disappointing but predictable. I also got some experience in "education diplomacy," talking with mothers whose children had not passed whichever test they were taking. Not my first taste of it though; I have a few semesters' experience in dealing with college students in the Math 108 course.

22:01

2006-04-11T22:58:00.000-06:00

Today was the first day of classroom observation after taking a week off for Spring Break. I got a lot of solutions written during that week, but it's good to have the interaction with students again.

Today was also my first day doing a tutoring job with a couple of homeschoolers. They are doing a highschool/college transition program called Running Start, and I today we went over an algebra placement test. They know how to solve linear equations, but need practice with them. A new concept for them was weighted averages. We also got on a rabbit trail about sums of infinite series when one of them asked what the sigma symbol on my calculator meant.

This evening I went to a Bible study. The church has two midweek studies, one on Tuesday and one on Wednesday. I figured the Tuesday one would work better because I've already got stuff going on that day. It's nice to have other days in the week with nothing specific to do but write solutions, because there's a certain amount of acceleration time when I start writing them. Once I get up to speed, I like to stay in the groove for the long haul, to mix a few metaphors. I rode to the study by bicycle (four miles into town, and one more to get back out of town in the other direction), but got a ride back because I don't have a reflective thingy to wear yet and because the back went flat on the way there. The study is right at the end of Galatians; tonight we talked about 6:6-9. I just looked up what the verses were in the little green Gideon New Testament/Psalms/Proverbs that was sitting on my desk, and was reminded again just how non-user friendly those things are. It's a pain to flip through the pages or hold open in a particular spot, and the positioning of Psalms and Proverbs *after* Revelation (plus the absence of all the other books) means that when I open to a spot that ought to be near Galations, I find myself in the middle of Psalms instead. The study was good, and the group is small enough that I'll be able to get to know people. It's kind of weird, trying to transition into being in the "adult" crowd rather than part of a "college group". Although, judging from the makeup of the congregation, I'll probably end up helping with the high schoolers.

Seeing how I've got so much stuff happening on Tuesdays, I think I'll start riding the bike in on Tuesday mornings, leaving it at the house where I tutor, then picking it up again later. That way if I have anything to do in town I can do it at that time, before riding back. It's too bad I can't take my job with me when I leave the house. In a lot of ways it's like doing homework for a living, but this is homework that has to be typed and illustrated.

Word for the day: Octothorp. And what is an octothorp, you ask? It's this: # The name comes from the eight points around the perimeter.

Fact for the day: If there were mile markers between the Milky Way and Andromeda galaxies, placed every 10,000 miles, there are enough ants on our planet that you could place one ant on every mile marker, if you didn't mind using them all up.

22:55

2006-04-06T23:40:00.000-06:00

I have a working bicycle that I can ride now. Pedaling four miles is a bit more than I'm used to doing, despite all the hiking up in the hills I've been doing lately. Riding against a headwind doesn't help any. It'll take some time before I can maintain the 12 mph necessary to make the trip in just 20 minutes, or the 16 mph necessary to do it in 15 minutes. At any rate, this will make it easier for me to attend a mid-week Bible study and that sort of thing.

20:37

2006-03-28T21:37:00.000-07:00

One perquisite of this job is that I have access to Adobe Illustrator. I discovered recently that it can make regular polygons on demand, and this led me to renew my interest in tesselations. One thing the program won't do is make said polygons with sides of a specified length; instead it makes them with a specified radius, which is the distance from the center point to a vertex. So in order to make different polygons with sides the same length, I had to do a little bit of trig first to approximate the radii.

I am specifically interested in tesselations of the plane using equilateral triangles, squares, and regular hexagons. Each of these can tesselate the plane if used alone, but there are a lot of interesting tesselations using combinations of them. There are infinitely many such tesselations, but I've been trying to find a way to catalogue the repeating ones. My current approach is to start with certain "base shapes" formed by taking a polygon, adding another polygon to each of its sides, and also adding any polygons that are definitely determined by these. For instance, if you have a 90 degree angle, the only thing that can go there is a square. I believe I have drawn all of these, and there are 10 with triangles in the center, 15 with squares and 28 with hexagons. (I'm not counting reflections and rotations.) It surprised me that only 6 of these 53 shapes have no lines of symmetry. There were some possibilities that I didn't draw because they wouldn't allow for eventual tesselation; namely, a hexagon and a square cannot be placed on adjacent edges of a hexagon, because the angle between them would be 30 degrees.

The next step will be to see which of these basic shapes can tesselate by themselves.

17:50

2006-03-24T18:48:00.000-07:00

Yesterday was interesting. I took the bus to meet Mr. Nickel to go do classroom observation at the private school, but he never met me at the bus station. Normally I go there on Tuesdays, but since there was no class on Tuesday I assumed we'd do it on Thursday, the same as last week. He failed to make this assumption. So, I took the 9:15 bus back, leaving me with about 2 1/2 hours to kill before Mr. Eby was expecting me back. Since he wasn't in the office, I left my bookbag there with the secretary and used the time to explore the town a bit, get a haircut, and eat brunch. It took me a long time to find a place to get a haircut, and I apparantly found the only barbershop in town. It being a tourist town, they also sell antiques, and the inside does not look like a barber shop. The chair you sit in to get a haircut is itself an antique; it is over 100 years old, but still in good enough condition that they use it every day. The lady said some people are horrified to learn they're using it as opposed to putting it behind glass, but she said after all that's what it's made for, adding that they'll sell it if they run into an interested buyer willing to pay a lot of money. I noticed that they had gold stars for sale that were shaped like stellated dodecahedrons. I have a Christmas ornament that looks similar in design but is a stellated icosahedron.

22:22

2006-03-19T14:14:00.001-07:00

Okay, more about that Fibonacci variant. You've got an infinite sequence, right? It looks like this:

1, 1, 1, 2, 3, 4, 6, 9, 13, 19....

For any given number other than the first three, f(n) = f(n-1) + f(n-2). So I was wondering: Is it possible to tack numbers onto the left, so that the pattern continues to hold? Consider:

X, 1, 1, 1....

For the pattern to hold with the third 1, we need 1 + X = 1. Which gives X = 0. So now we have:

0, 1, 1, 1, 2, 3, 4, 6....

Tack on another one, and we get:

Y, 0, 1, 1...

So Y + 1 = 1, yielding Y = 0, and:

0, 0, 1, 1, 1, 2, 3....

Carry this process out a few more terms and you have:

....-1, 5, -3, -2, 3, 0, -2, 1, 1, -1, 0, 1, 0, 0, 1, 1, 1, 2, 3, 4, 6, 9, 13, 19....

Doesn't it seem weird that on the righthand side the sequence is monotonically increasing, probably with all positive derivatives, but on the lefthand side it's so chaotic?

The same sequence that's being generated off to the left can be formed in its own right with the following definition:

f(0)=f(1)=f(2)=1
f(n) = f(n-3) - f(n-2), n > 2

Thus for the first few terms we get:

1, 1, 1, 0, 0, 1, 0, -1, 1, 1, -2, 0, 3, -2, -3, 5, 1....

I've carried it out some distance using a calculator, and the numbers continue to fluctuate between positive and negative. The also seem to be generally increasing in absolute value, but it periodically dips back close to 0 as well, which means that it may have convergent subsequences as well as divergent ones in both directions.

13:15

2006-03-19T14:14:00.000-07:00

I went to a church this morning that looks like it will be where I continue to attend for the rest of my time here. I've never been in the position of having any difficulty choosing where to go to church before. I went with the couple I'm staying with the past two weeks and wasn't sure whether I should continue doing so, but had been hesitant about looking around because I hated the idea of going a different place every week and trying to compare and decide. However, the church I went to today is a good place for me for a few different reasons. One of the three elders (and I think the one who does most of the Sunday morning teaching) is a graduate of The Master's Seminary, which is connected (organizationally, not geographically) to The Master's College, where I went to school as an undergraduate. Another guy who attends there was actually in my graduating class at TMC, and lived in the same dorm as me. It's also a fairly small church, about 100 people, which is what I'm the most comfortable with. It makes it easier to get to know people, and easier to get involved in things other than just Sunday morning. Another factor making it easier for me to get involved is that it's in the town I'm close to, rather than the one 20 miles away. And, well, it felt like coming home. It is a church family I can really be a part of.

23:53

2006-03-18T00:52:00.000-07:00

Okay, so I'm going to try and start this up again. I have officially relocated to Washington state, and am employed in writing a solutions manual for Mathematics: A Human Endeavor by Harold R. Jacobs, which is a pre-algebra text. The job provides room and board, and I live in an apartment which is attached to a house; one of the guys I'm working for and his wife live downstairs. They also own a vacation home rental business. On Tuesdays (or sometimes Thursdays) and Fridays I do classroom observations, where the curriculum I'm writing solutions for is being field-tested in classrooms (some at a private school and some with homeschoolers), in preparation for filming video lectures. The rest of the time I work from my apartment.

Today I got to give the last half of the lecture to the third homeschool class, which consists of two girls taking prealgebra. I was trying to help them review for a test, and we were going over conic sections. Not having seen the lectures on this material, I was mostly guessing from what was in the review section (no pun intended). In trying to explain the basic concept of conic sections, I used a styrofoam coffee cup as a prop. It's not quite a cone, but its convex hull is a truncated cone and imagination can supply the rest.

Chapter 2 of this Jacobs text is about number sequences. Earlier I was revisiting a number sequence that I've played with in the past. It's a Fibonacci variant which seems to me to be pretty obvious, but I've never seen it mentioned anywhere:

f(0) = f(1) = f(2) = 1
f(n) = f(n-1) + f(n-3), n > 2

1, 1, 1, 2, 3, 4, 6, 9, 13, 19, 28, 41, 60, 88, 129, 189, 278, 407, 596, 874, 1281...

Compare this to the original Fibonacci sequence, also carried far enough to hit four digits:

f(0) = f(1) = 1
f(n) = f(n-1) + f(n-2), n > 1

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597....

One interesting thing about the new sequence is that any two consecutive numbers after the first three are generated by adding two completely different pairs of earlier terms. The sequence can actually be generated by a story problem similar to the original one with the rabbits. Fibonacci's rabbits took one month to mature, and reproduced a new pair every month thereafter. The new rabbits take two months to mature, but still reproduce at the same rate after doing so. Using * for a pair of baby rabbits, r for a pair of juvenile rabbits, and R for a pair of adult rabbits, the first few iterations look like this:

*
r
R
R *
R r *
R R r *
R R R r * *
R R R R r r * * *
R R R R R R r r r * * * *
R R R R R R R R R r r r r * * * * * *

Again, compare this with the original problem, where the intermediate stage does not exist:

*
R
R *
R R *
R R R * *
R R R R R * * *
R R R R R R R R * * * * *
R R R R R R R R R R R R R * * * * * * * *
R R R R R R R R R R R R R R R R R R R R R * * * * * * * * * * * * *

It is of course possible to make other, similar modified problems of the form:

f(0) = f(1) = ... = f(k) = 1
f(n) = f(n-1) + f(n - k - 1), n > k

For the original Fibonacci sequence, k = 1, and for the modification shown above, k = 2. Any such sequence would model a rabbit population where the time required grow to maturity is k times the length of a reproduction cycle. It's late now so the rest of this will have to wait.

18:53

2006-02-13T18:52:00.000-07:00

I've taken the job in Washington and will probably be going there in two or three weeks. It is an internship with an organization that is producing various educational materials written from a Christian worldview perspective, mostly for use by homeschoolers. What I will be doing is mostly writing solutions manuals for mathematics texts. The job will last 9-12 months, but could possibly lead into something more long-term. Either way, it will be a good experience.

10:19

2006-02-03T10:17:00.000-07:00

No news about the job yet. I'll report on that when I have something to report.

The board game has gone through a series of revisions and version 3.0 is close to being completed. Qalmlea volunteered to design the cards for me on Printmaster, which means that they have been getting designed rather than waiting to be designed while I think about other things. I don't think I'll have a new version ready to go tonight, which means Erik will even more disappointed that he played Heroscape last week instead. I wasn't anticipating that my most enthusiastic beta tester would be a twelve-year-old, but there you have it.

I've read a few more chapters in War and Peace. I anticipate finishing it this decade. It's rather hard to keep track of the various characters, so I'm probably missing some plot flow. I keep thinking it ought to be the first book of a trilogy. The second one should be called Freedom and Slavery, while the third should be called Ignorance and Strength. Long live INGSOC.

My roommate has been reading the Chronicles of Narnia, and is on the third book. (The Horse and His Boy, reading them in the order of the timeline within the story.) He seems to be taking to them quite readily for someone who never read much fiction. When he was a kid, he read encyclopedias and technical manuals.

Speaking of Erik (which I did three paragraphs ago), I have to figure out what to do with my Sunday school class next week. Week after next, we start the new curriculum, and last week we finished the old. I had thought we might do Ruth in two lessons, but it was no problem to finish it in one. I could make cookies again. That would eat up some time, pun intended.

My shift starts in 20 minutes. I'm scheduled to get off at 16:00 today. That would be kind of nice. It isn't likely to happen, though. We're a bit shorthanded and I'm typically asked to stay until 17:00 even if I'm not scheduled that late. I don't really mind the hours; it just would be nice if the schedule reflected reality more closely.

11:14

2006-01-28T11:16:00.000-07:00

We had an employee meeting at Taco Bell this morning from 7:00 to 7:25. Various new policies (and/or revitalization of old policies) were discussed, but it sounds like the two things which affect me the most are:

1) The greeting of a customer in the drivethrough is now standardized. I must say, "Hi, how are you?" Those precise words must be used; variations are no longer allowed.

2) Every customer who does not either order a drink or specifically say he or she does not want one, must be offered a drink. This has actually been standard ordering practice for a while, but it's being emphasized because failing to offer a mystery shopper a drink is now going to be grounds for failing the test. The annoying thing is that the drink must be offered even if the customer is only ordering cinammon twists, and even if it's the same customer at the front counter adding one more item to a larger order which was handed out a few minutes earlier. This sort of policy appears to be designed to irritate customers.

In other news, I'm supposed to have a job interview by phone today. But I don't know at what time the guy intends to call me. Since getting out of the meeting I've been hanging out on campus so as not to disturb my roommate who is quite possibly still asleep. This would be a fine place to do the interview, but for all I know he's not planning to call until this evening.

10:43

2006-01-19T10:44:00.000-07:00

I'm back in town and working on stuff for a job I'm applying to. More details later.

I've also created a board game, which is mostly constructed. It involves wizards, lizards, and giant frogs. It was influenced by the game Heroscape and the books Eragon and Eldest by Christopher Paolini, but bears little resemblance to either. Perhaps if the wizards had dragons and the lizards and frogs were Urgals. Changing the creatures to Urgals wouldn't be that hard, if I had miniature Urgal figures -- the only reason they are lizards and frogs is because that's what the dollar store had available. Dragons, however, would seriously complicate things. Don't they always?

Last night I had two dreams that I can remember. The first involved me setting out to visit my old college for Alumni Weekend (which in real life is either coming up or else just passed) but ending up at the place where I used to go to summer camp instead. I got there late Thursday afternoon, and it turned out that the camp was having Alumni Thursday that day, so it worked out great. I was very tired when I arrived and wanted to just to take a nap, but they insisted that I participate in a bunch of games outside which went late into the night. Then I had to find a cabin. The new one that used to be the nurse's station was full, and they said that I couldn't stay in any of the original ones, making vague references to an evil swamp. So, I had to go find the *other* new one (which doesn't really exist). It was located deep in the forest, well outside the real boundaries of the camp, and was rather difficult to locate in the dark as there were no paths leading to it. I got to where it was supposed to be, but there was nothing there but a coffin. Someone else was with me, and we were arguing over who would get to sleep in the coffin, when we realized that there was already a dead person in it so we couldn't.

In the other dream, I was taking orders at Taco Bell, which is what I have to go do right now.

13:34

2006-01-05T13:32:00.000-07:00

After visiting my family for two weeks, I go back home tonight. Someone called from Taco Bell this morning; apparantly the manager scheduled me to work at 11:00. I thought I had written down that I wouldn't be back until the 9th, to be sure I'd be in town before then. At any rate, I work tomorrow at 11:00. My roommate and his sister are planning to leave at 19:00 tonight. That means I'll be able to go to at least part of the boys' basketball game with my sister. Probably all of it, by the time they actually are ready. The plan is for them to pick me up at the gym, which is closer for them anyway.

13:42

2006-01-01T13:41:00.000-07:00

More about Set theory.

Suppose you have a collection of cards which do not contain any Sets, and you want to know the probability of randomly adding one more card and getting at least one Set. For any two cards in your collection, there is exactly one third card that, when combined with them, will form a Set. At first glance it might appear that for N cards, there would be (N choose 2) different cards that could be added which would make at least one Set. The trouble is that it's possible to have two (or more) different pairs of cards in your collection, all of which need the same card to complete them. If there are four cards, for instance, there can be either five or six new cards, each of which would form a set if added. It's possible to do all the calculations by brute force on four or five cards, but then it gets really really complicated.

16:29

2005-12-29T16:29:00.000-07:00

My sister has a card game called Set. Each card has a picture on it, which can be uniquely described in terms of four properties. Each property has three possible values. The deck has exactly one card with each combination of property values, giving a total of eighty-one cards. To play, you deal twelve cards face up, and then everyone looks for "Sets". A Set (capitalized to distinguish it from the math term) consists of a (lowercase) set of three cards which are either all the same or all different with regard to each of the four properties.
When someone identifies a Set, they remove those cards from the table and three more are dealt. If there are no Sets available, then you deal an extra three.

I had played this game once before, and thought I was competent, but no one comes even close to competing with my sister. She usually sees Sets before I have a chance to start thinking. Anyway, that's not what I'm posting about.

The instructions made claims about the probabilities of not having a Set when there are twelve or fifteen cards on the table. Over the past few days, I've tried to verify these figures mentally and have had much more difficulty than I anticipated in determining how many sets of a given size can be constructed which contain (or do not contain) a Set. I think I'm going to be obliged to work this out on paper.

A couple of interesting ideas:

For any given pair of cards, there is exactly one card which can be added to form a Set. Any given card is therefore a member of exactly forty Sets. This gives rise to an equivalence relation on pairs of cards, where two pairs are equivalent if they require the same card to make a Set. There are (81 choose 2) = 81*80/2 = 81*40 pairs of cards, which are thereby divided into 81 equivalence classes with 40 elements each.

22:54

2005-12-22T22:54:00.000-07:00

I went to my sister's basketball game tonight. It was a very close game, although her team was slightly ahead for most of it. The score stayed tied for several minutes in the last quarter, and the game went into overtime. Each team scored one freethrow point, and it stayed tied again for a while. Her team finally won by two points, at least one of which was also from a freethrow.

16:15

2005-12-22T16:15:00.000-07:00

I'm posting this from my mom's computer, since I'm visiting my family for a couple of weeks. Tomorrow my sister and I are planning to go finish our Christmas shopping together. Things are pretty much the same as I remember them here. The family cat is still the undisputed queen of the house. She's changed her habits slightly and will sometimes sit on someone's lap for as long as two minutes.

I'm just getting over a cold that I've had for most of a week. This prevented me from playing hockey, or at least that was my excuse, but maybe I was just being a wimp. After all, my roommate got hit in the lip with a rubber ball we were using for a puck, had to get five stitches in it, and went back and played again the next night. The nurse at the hospital was from Canada, and was disappointed to learn that we played without skates.

We still haven't decided when exactly we should open presents. Christmas morning has the disadvantage of being a Sunday morning, and we are supposed to go to our relatives' house (a ten minute drive) after church. I suggested either Saturday or Monday, so as not to be rushed either morning, but so far a concensus has not been reached.

Meanwhile, I'm looking at a movie poster for Holes which is attached to the side of my sister's locker (yes, she has a locker) so I think I'll end with a deep thought (pun intended): Hector Zeroni's nickname is "Zero", and the numeral 0 is shaped like a hole.

10:46

2005-12-15T10:46:00.000-07:00

I've made some alterations to the left sidebar, over there to the left.

<==

Most notable are the blog links. If your blog is not on there, it's because I have to leave for work in a couple of minutes, and I just put up the blogs with addresses that I have memorized. The reason I have them memorized is because I don't get to them via links on some other page. I plan to expand the blog list later.

19:26

2005-12-12T19:26:00.000-07:00

We played hockey last night. We do this at an outdoor skating rink, but just with tennis shoes, not skates. There were nearly thirty people by the time everyone showed up. After a while everyone not in our group had either left or been assimilated by us, so we played lengthwise and used the whole rink, since the teams were so big. I find it isn't that hard to keep my balance on the ice; what's hard is moving with so little traction. It takes a lot of effort to accelerate, and having accelerated, it is almost impossible to turn.

16:39

2005-12-07T16:35:00.000-07:00

Work was interesting today. The computer that is normally used by the person with the drivethrough headset has officially died, which makes doing the drivethrough considerably more challenging. See, it normally works like this: A customer gives their order to whoever has the headset, and that person enters the order into that computer. It simultaneously appears on three other screens: One for the drivethrough window cashier, who is preparing napkins, sporks, and such, another for the people on the food line, who are making the food, and a third for the customer, so they can doublecheck that it is right. When the headset person hits the "Store" button, that order gets sent to the other computer, which is attached to the drivethrough cash register. It then prints a receipt, and brings that order up on its screen when all the orders before it have been paid for and handed out.

Okay, so with the first computer out of commission, it is necessary to ring up the orders on the second computer. This has always been possible, because people sometimes add items to their order after they pull up to the window. If just one person is working over there, there's not much difference. The only time it is not possible to enter items to the new order is when you are taking cash for the one currently at the window. This is the case even when both computers are working, because it's not possible to stand at the window and at the other computer at the same time. One person can do both jobs, although things move a bit slower because almost every customer gets put on hold at least for a few seconds when it's busy.

The trouble is that when you introduce a second person, the computer is still tied up while cash is being taken. So the only way to speed things up is for the order taker (which was me this morning) to write down the orders on paper, so that the cashier can ring them in when the register is free. I got a fresh roll of register tape, and basically produced handwritten receipts for about two hours. These got replaced with printed receipts once the orders were entered into the computer. The system got more efficient once I figured out what order number I should be on and started writing the numbers at the top.

The other difficulty is that until the orders get entered into the computer, they don't appear on any of the screens, and with that computer they never appear on the customer's screen. This meant that I had to keep repeating orders back to the food line people so that they could make the correct items, as well as repeat each order back to the customer since they weren't able to look at it themselves.

It actually was kind of fun to do it this way, if a bit more stressful for everyone. It was hard for me to get all the drinks made since I had to be standing with my back to the dispenser while writing the manual receipts. I was rather pleased when the delivery truck arrived, and I had to give someone else the headset so I could go put everything away.

20:18

2005-12-06T22:18:00.000-07:00

Okay, I'm not in this semester's Modern Geometry class, but I have become mildly obsessed with one of their homework problems. The statement is simple enough: Given that the circumcenter of a triangle is the same as the Gergonne point, prove that the triangle is equilateral. The circumcenter is the center of the circumcircle, which is the circle that circumscribes the triangle, i.e., intersects all three vertices. It is also the intersection point of the perpendicular bisectors of the sides. The Gergonne point is defined as the point of intersection of the lines connecting the vertices with the points of tangency for the incircle, where the incircle is the circle inscribed in the triangle. The approach I've been trying is to show that when the Gergonne point and the circumcenter are the same, they must also be the same as the incenter, which is the center of the incircle. But I haven't had success yet. Apparantly no one in the class, including the teacher, has been able to solve this.

10:23

2005-12-02T10:23:00.000-07:00

Today the 2000th consecutive Schlock Mercenary comic strip was posted. I've been reading this comic ever since my friend Matt convinced me to read the archives, which took me about a semester to get through. It has become my second favorite comic that's still active, right after Foxtrot. It would probably be my favorite if it had more math jokes. Furthermore, the cartoonist has promised to post a list of sites mentioning this historic event. So, by making this blog post and emailing him about it, I should be able to get my blog in his list of links.

21:17

2005-12-01T21:17:00.000-07:00

I had my oral exam today, and I passed. So I now have a master's degree. It will be nice to be able to put that on job applications. They didn't ask me anything about Numerical Analysis, or Partial Differential Equations. Not too surprising, I guess. Those were pretty much applied classes and I picked theory people to be on the committee. I was glad that they did ask about Representation Theory. That was a fun class (in retrospect) and I enjoyed reviewing the material.

Most of the test focused on the three courses that I took full year sequences in; namely, Real Analysis, Topology, and Modern Algebra. Most of the topology questions were on point-set topology, because Dr. Stowe didn't realize that we did a lot of algebraic topology second semester. As a result, he asked me about fundamental groups but not about homology groups, since he was just asking stuff off the top of his head once he realized that algebraic topology had been covered. The most involved proof they asked me to do was in point-set topology; namely, to explain why any infinite sequence of points in a compact metric space must have a cluster point. It's not a complicated proof, given some preliminary stuff that we had already talked about, but given the fact that I didn't actually look at this proof while studying, it was rather involved to come up with extemporaneously. Then he asked me the difference between a cluster point and a limit point, which was ironic because the whole time we were talking about cluster points, I was trying to think how the two concepts were different, and hadn't figured it out. After thinking about just that for a few moments, I realized that I was reading a condition into the definition of cluster point that wasn't there. Hmm, I just realized that I failed to answer one question that he asked in that regard. I answered a related question, and then he said something like, "That's close enough; let's move on." Huh. I still don't know the answer. What he actually asked was whether something like the Bolzano-Weirstrauss Theorem applies to an arbitrary compact metric space. He asked it in such a way that implied the answer is no. I'll have to think about that one.

When we got to Modern Algebra, Dr. Hill pointed out that all four questions I skipped on the written exam were about Field Theory, and then proceeded to ask all Field Theory questions. That part of the exam didn't go so well. At least she didn't ask about Galois Theory.

After it was all over, the outside committee member, who was from the business department, commented that the only thing she understood the entire time was the term "function of x".

17:39

2005-11-30T17:40:00.000-07:00

I have a new favorite customer complaint. A woman drove up to the drivethrough window, and I gave her what she ordered, which included a large drink. When I realized she wasn't leaving, I opened the window again to ask what she wanted. She held up the drink and said, "When I said 'large,' I meant 'large large'. Do you have a size bigger than this?" The term is extra large, in case anyone was wondering.

22:31

2005-11-29T22:30:00.000-07:00

Ha! I updated again!

Last night when we got home, Jeremy and I discovered that our bathroom ceiling was leaking again. Last time the maintenance people determined that it was caused by the neighbors upstairs overflowing their bathtub. It leaked more rapidly this time, so I was a bit concerned that it might continue and felt justified in calling the emergency after-hours maintenance phone number. You're only supposed to call it if there's an emergency, which would probably make some sense if anyone was around to answer it. However, all it actually does is connect you to the emergency after-hours maintenance answering machine, where you can leave a message, after which they will get back to you within a week. Fortunately, the ceiling stopped leaking after a while, but there is a small hole in it now and a larger soggy area.

20:38

2005-11-28T20:38:00.000-07:00

In response to the more recent comments on my previous post, non-linear posting means I won't wait to make a small post just because there's a big one. However, it doesn't stop me from being distracted away from *all* posting, for whatever reason. In this case, my oral exam is on Thursday.

Today I wasn't supposed to work except for tutoring, which would have meant that I could study pretty much all day. Then this morning I got a call this morning asking if I could come in from 11:00 to 14:00. Okay, three hours didn't sound too bad. This turned into five hours once I was there, and would have been six hours if I hadn't kept asking to leave. Then somehow I was inconveniencing everyone, because a different employee had to stay late so that I could leave "early". I have yet to think of a reasonable definition of "early" which makes sense when I left two hours after I was supposed to stay on a day when I wasn't even scheduled. The employee who stayed late was offered free food as an incentive. I was not. Okay, I'll stop complaining now. I shouldn't have answered the phone on my day off when I saw it was Taco Bell.

A Tribute to Non-Linearity

2005-11-09T21:45:00.000-07:00

In the interest of not having the gaps in my blog approach infinity, I'm going to start blogging non-linearly when necessary. In other words, if I have a big post to make then I won't wait on it before making smaller updates. Doing things out of order like that bothers my sense of order and propriety, but I figure I can adjust. In order to prove that I'm capable of altering routine, I've given this post a title instead of a time signature. And I'll follow with a rambling update about various details of my life:

I put away the truck shipment at Taco Bell today. It was a relief driver because the usual guy hurt himself. After I got the freezer stuff put away, he moved one stack of boxes up against the freezer door in order to make more room. This seemed to make sense until Logan, who was doing backups, needed to get something out of the freezer.

I had a dream the other night in which I was with several people in a house, and we were all working quickly to barracade the doors and windows. They said there was a wolverine outside trying to get to us. I said that they were overreacting; wolverines are fierce but not that fierce. Then I saw the thing. It walked on two legs, and was three or four feet tall. It had claw-like hands, and was covered in short brown fur. My first thought was, "That's got to be a CG creature, not someone in a costume." Then I remembered that it was real. (This was not a lucid dream.) I said out loud that it was definitely not a wolverine. Someone asked, "Then what is it?" I said I didn't know, and they said that if I didn't know what it was, then I couldn't be sure it wasn't a wolverine. Whatever. It looked intelligent, wicked and dangerous; it was definitely hunting us. Good thing we blocked the entrances.

I now have five students, and three of them have rescheduled at least one tutoring session over the next week. Much more of this and I'll have to start writing my schedule down.

Speaking of tutoring, does anyone remember how to do this kind of problem?

lim(x=>infinity) x*tan(1/x)

Obviously 1/x goes to 0 so tan(1/x) goes to 0, so you end up with infinity*0, an indeterminate form. Given the chapter it was in in my student's calc book, I suspect they need to do some kind of trick to turn it into a form that's valid for L'Hopital's Rule, but I can't think how to do this offhand. They didn't need to know right away so we didn't pursue it when I couldn't solve the problem immediately.

In my Sunday school class, we are up to Joshua 8 or 9 (whichever starts right after the conquest of Ai). I've stopped following the lesson plans so precisely. Joshua has more chapters that I want to cover than the notebook outlines, and I always used to finish early, so I've started just moving through the material until we run out of time. So far we've kept pretty much on schedule; I think we'll finish the book in the prescribed number of weeks. I'm still skipping a large portion in the middle of the book -- 12 to 22 or something like that -- that mostly talks about tribal allotments. I'll show the kids a map of Israel with the tribal borders drawn in and the tribes labeled and figure a picture is worth several thousand words. Granted, we wouldn't be able to construct such a map without all those words, which is part of why they are important, but I don't feel the need to read through it all with fifth and sixth graders.

A few nights ago I wrote a three or four more paragraphs on the next chapter of my fantasy story. I'm gearing up for a couple of major shifts in the plot; I know where one of them is going, but not the other. It will be interesting to see how it plays out.

My roommate's learning to play the guitar, and he obtained sheet music for several Simon & Garfunkle songs. I'd really like an explanation of the first verse to song The Boxer by Paul Simon:

"I am just a poor boy, though my story's seldom told. I have squandered my resistance for a pocketful of mumbles; such are promises. All lies and jest, still a man hears what he wants to hear and disregards the rest."

Can anyone explain to me what it means to squander one's resistance for a pocketful of mumbles? I've double checked the lyrics; the word is "resistance" not "existence". I couldn't find anything useful on the web.

As long as I'm trying to make sense of Simon & Garfunkle lyrics, how about his verse from The 59th Street Bridge Song?

"I've got no deeds to do, no promises to keep. I'm dappled and drowsy and ready to sleep. Let the morningtime drop all its petals on me. Life I love you! All is groovy."

What does it mean to be "dappled and drowsy"? I know what "drowsy" means, but "dappled," I thought, meant variegated in color. Usually it's used to describe a speckled horse.

Okay, I'm done rambling.

17:42

2005-10-09T17:42:00.000-06:00

I haven't forgotten about this blog; I'm planning to update it soon. But the update will take a little time and I'm usually online for fairly short periods lately.

20:08

2005-09-14T20:07:00.000-06:00

Wednesday is now my big tutoring day. I have a student from 16:45 to 17:45, then three students in a row from 19:00 to 22:00. I ought to be tutoring the second student right now, but he hasn't shown up. He was notified of the time on Monday, but maybe he's one of those people who doesn't check email regularly. It's kind of a pain, because I'm meeting the 21:00 student downstairs in the same building. I don't want to just hang out here for an hour, but if I go anywhere else I have to come back. And I don't have any math books with me, because I was expecting to spend the whole time tutoring.

Random fact: You only need basic math skills to be a pet groomer. This is according to a poster here in the math lab, which shows what level of math is necessary for various careers. It also says that to be a computer programmer, you need "three to four years -- more math in college". But I'm not sure if I'd trust what the person who made this poster says about computer programming. The cartoon illustration shows a woman writing some kind of Star Wars game with a Tie-Fighter in it, but the screen is just covered in ones and zeroes. That's more low-level than machine language. I'm not sure if anyone has ever programmed like that. Also, her hands are on the main part of the keyboard, not the numerical keypad. In fact, looking closely, it doesn't have a numerical keypad. And it's only got three rows of keys, so it doesn't even have a top row with numbers. So how is she typing all those ones and zeroes? Her computer doesn't have a mouse, either. I guess it doesn't need one.

14:49

2005-09-13T14:48:00.000-06:00

Today they put me on expediting with just one other person on the food line. And they started training Adam on the drivethrough register. Considering we were both inexperienced, it was pretty impressive that our average time was around 1:05. Cruchwraps are still the most fun things to make.

21:11

2005-09-12T21:10:00.000-06:00

It's always hard to get this thing updated again after leaving. Um...family camp was good. My roommate's family (all 11 of them) went. There were a lot of people there this year, and not just because of that. We probably had between 50 and 100, at a guess. It was good to get away from the usual routine, and I always enjoy spending time with those guys. On Saturday night we played board games. I played The Farming Game for the first time -- it's a lot more fun than I thought it would be. I also brought Clue: The Great Museum Caper, which was a big hit.

Another thing that's been going on is tutoring. I now have a calc I student on Monday and Wednesday evenings, and starting this Wednesday I'll have a second student on those days, but I haven't found out what class he's in. I've also probably got a basic algebra student early on Wednesday evenings, and another potential calc I student for I'm not sure what time.

This week was Promotion Sunday, when they move all the kids into their new classes. I lost four or five and gained that many or more. This week I had nine students. I think I've only got two boys. Eric is really glad that Bradley moved up, since John, Torey and Jordan are all in Junior High now. The new curriculum is starting in Deuteronomy, and will continue through Joshua and Judges, finishing up with a series of lessons on the birth of Christ (which will happen around December). I tried something new this week: I had each of the kids take turns reading part of the passage. Some are better readers than others, but they were all coherent. It think I'll keep doing that; it engages them more. I also need to talk to the boys about not whispering when someone else is reading.

They tried to teach my how to take orders at Taco Bell today. I took one inside order and accidentally punched it up as a drivethrough order without noticing. That created a minute or two of panic when someone figured it out.

10:37

2005-09-02T10:36:00.000-06:00

I'm going on a church camping trip this weekend. I might be online sometime later today, but after today I'll be gone until Monday or Tuesday.

21:21

2005-08-31T21:20:00.000-06:00

I found out today that it doesn't matter if the actual amount tendered gets entered into the cash register, as long as the correct change is given. So if I can calculate the change faster than it would take to punch the numbers in, then I can just hit the exact change button and open the drawer quicker. The helps shave a few seconds off the drivethrough time, in an effort to get the average down. Today the average was 58 seconds when I left. That's better than yesterday, when it was over a minute. Of course, yesterday they were training a new guy on food.

Also, I've finally stopped my brain from starting to find prime factorizations every time an order number gets called out. But if you walk up to me and say a random integer, it will still do that.

16:51

2005-08-29T16:50:00.000-06:00

I ended up making cookies for the Sunday School class. I called and got a recipe from my sister on Saturday. They didn't turn out quite how they were supposed to, but I think I know what I did wrong. As it turned out, most of my class was gone yesterday; I only had 3 girls and no boys. We ate some of the cookies and played a board game.

Sunday afternoon my family came and visited. They took myself and my roommate out for lunch/dinner at Red Lobster. (My dad has been wanting to eat there for a long time and finally talked my mom into it.) Afterwards we discovered that the mall was closed, then went to the zoo for the last ten minutes that it was open. Ultimate Frisbee was at 19:00 since the high schoolers were coming back from a camping trip, and my sister played with us for about an hour until my parents were ready to leave.

Today at work I was the drivethrough cashier again. I like that job.

I have emailed Dr. Hill about oral exam and will hopefully be able to schedule it soon.

16:15

2005-08-26T16:14:00.000-06:00

Last night was the first Crossroads (college group) meeting. Dan is taking over leading it, but Brad is still leading the music. It was just an introduction to what we do there and that sort of thing. There were a lot of newcomers; I counted 42 people in the room total.

15:15

2005-08-25T15:14:00.000-06:00

Someone called in sick today so I ended up being the drivethrough cashier instead of working on the food line. Despite working in restaurants before, this is the first time I've handled a cash register. This one has a touch-sensitive screen, which is a bit tricky to work with until you get the hang of it. Basically I was just taking money, making change, and handing out food for four hours. I was doing pretty good until one lady gave me three dollars in change. I had to count it, and that backed everything up. Naturally there were several cars behind her. The goal at Taco Bell is to average 45 seconds on drivethrough orders. I'm sure we were over that today.

10:09

2005-08-25T10:08:00.000-06:00

A few random items I forgot to mention:

Random Item #1: Monday at Taco Bell, some lady in the drivethrough asked for a "rice meal". After consulting with the other workers, the person with the headset told her, "we don't have any meals with rice". Her response: "Yes you do!" This reminded me of when customers at Gertie's would insist that we had cream cheese pizza or jalapeno pizza. The lady also wanted ice cream, which Taco Bell does not have.

Random Item #2: I have to plan an end-of-the-year Sunday School party. I asked the kids for suggestions, and they seem to want a big review question game with candy for prizes.

Random Item #3: Since I'm not taking classes this semester, I had to move out of my office. Eight boxes of math books. Right now they are sitting in the living room until I can figure out a way to make room for them somewhere else.

15:56

2005-08-24T16:56:00.000-06:00

This post about the backpacking trip has been sitting as a draft waiting to be completed for several days:

Where to begin? I obtained a backpack on Thursday afternoon and spent most of the rest of that day organizing my gear and packing it up. I believe it was lighter this year than last year, even with the added weight of a tent. Before I strapped the tent on, Mike estimated that my pack weighed about 33 pounds. The tent wasn't very heavy; it was the little two-man one that Kevin and Torey used last year.

The drive to the trailhead was long. We took off around 11:00 and didn't get started on the hike until about 17:30. We picked up my roommate Jeremy on the way. The hike itself took about 2.5 hours. It was five miles, but only the last mile and a half were very steep. There were twenty-four of us (up from sixteen last year), so we got pretty spread out. At one point Kevin, who was in the very back, shouted instructions which got passed from group to group, and apparantly distorted on the way. What I heard and passed on was, "Bear right at the top of the falls!". I assumed that this meant to turn right upon reaching the top of the waterfall, although it could also be interpreted as meaning that there was a dangerous animal sitting right at the top, or possibly that we were supposed to go skinny dipping there. As it turned out, the instructions should have been, "Cross the river at the bottom of the falls!". As a result, some of us ended up taking a more difficult route than was necessary.

The Barry, Mike, Steve & Company, as usual, got to the trailhead a long time before anyone else. In fact, they first got to the lake around the time we were starting out. After the first arrivals showed up, they hiked back down to help stragglers. I think Mike carried about five backpacks up the steepest part of the hill.

After arriving, the first order of business was to decide whether to eat dinner or set up the tent first. Jeremy was predictably campaigning in favor of dinner, but I wanted to find a good campsite before it got dark. He agreed to this and we found a place to set up. Andrew and Phillip pitched their tent in the same area. As I said, it was Kevin's little two-man tent. It doesn't look big enough for two from the outside, but inside there is room enough as long as you don't try to do anything except lay down. Rolling over in the night, sitting up, putting on your shoes, etc. are not recommended activities.

In order to pack more lightly, I took a couple of freeze-dried meals. They aren't bad, and they are easier to prepare than Ramen noodles. Jeremy brought vegetables and raw hamburger, which he wrapped in foil and cooked on the coals. He also brought a piece of raw dough which he cooked on a stick the second night. He said it wasn't bad. On Sunday morning there wasn't time to cook anything, so he ate a raw potato with salt, and leftover Smores ingredients. My roommate has interesting ideas about food. I have yet to see him turn down food when it is offered, under any circumstances. He says this comes from living in a large family. You learn to eat food as soon as you see it, before it disappears. The younger children only survive long enough to learn this because they are cute and the older siblings take pity on them.

On Saturday, we hiked up to the second lake, where some of the guys jumped off the cliffs into the water, then swam out to a rock, about 50 yards away. John, who is almost 13, swam out there, but it took about half an hour to convince him to swim back. He finally went along with a couple of older guys, and grabbed onto them for part of the way. Everyone said the water was freezing in that lake, but comparatively warm in the lower one.

We ate lunch up there, and afterwards some of the guys were going to hike up to the third lake, and then to the top of the highest local peak. I was inclined to just go back to the lower lake, and I decided to do this for sure because Kevin wanted to go on the day hike, but needed an adult to stay with Torey and John. So, I followed the boys back down to the lower lake, where they went swimming. After a while Mike, Tommy and Aaron joined us. John displayed his amazing powers of irritation, prompting us to threaten to throw him in the lake -- which didn't mean much since he'd been jumping in. A few other threats were made, and he at least stopped throwing big rocks in and splashing everyone.

That evening we gathered at one of the campfires and discussed an article everyone had been given copies of; it was a chapter of the book Holiness by J.C. Ryle, which is actually a collection of sermons. The chapter we read was about love for God as a foundational aspect of Christianity.

As everyone was showing up, there was a full-grown doe that wandered down near the campsite and stayed there grazing. She would perk up and listen every time there was a loud noise, but didn't seem concerned with all the people. Martin, who is from West Africa, had three questions about the deer: 1) What is it? 2) Is it dangerous? 3) Who does it belong to? He's been in the U.S. for five years, but there's still a big culture gap.

The hike down was in some ways more difficult than the hike up. Not as tiring, but more tricky in the steep places. For a while I was by myself, then I ended up with Andre, who was guiding Torey and John. There were places where we would just pick a tree below us, then basically do a controlled slide and stop ourselves by running into / grabbing onto said tree. The nice thing was that on the way down the hard part was all in the beginning; then it was pretty much just a level hike until we got back to the trailhead. Not everyone ended up in the same place at the bottom of the hill, and it took most of an hour to locate everyone and make sure we were all accounted for.

I'm sure there's other things I could have typed, but I just want to get this posted finally.

16:44

2005-08-24T16:44:00.000-06:00

Now that the backpacking post is up, I have other news. I found out on Monday that I passed my algebra exam. Now I just have to schedule and pass the oral exam.

Also on Monday, I had the orientation for my new job at Taco Bell. None of the teaching jobs I applied for worked out this fall, so I'll probably be hanging out here for another semester at least. I started work yesterday; for the time being I'm working Monday-Friday, from 11-15. Today I was offered an additional morning shift doing outdoor cleanup, but I want to see if I can do some tutoring or something in the mornings, since my schedule at Taco Bell is going to be predictable.

15:14

2005-08-11T17:13:00.000-06:00

Well, I've got the backpack, and the sleeping bag, and the food. Now I just have to put everything together. Sure was hot today.

20:22

2005-08-10T20:21:00.000-06:00

Not a whole lot going on. I haven't heard back yet from either the college I'm applying at about my application or the graduate committee about my test results. This weekend I'm going on the men's backpacking trip with some guys from my church. Today I got a haircut.

Hmm, I guess I haven't mentioned Sunday School lately. The girls have started actually participating, so that it feels like a real class. We just finished Numbers, and have a few weeks before the fall curriculum starts, so starting Sunday after next I'll do some review.

15:19

2005-08-05T15:18:00.000-06:00

Well, I took the exam today. Four hours of algebra! Some people would consider that torture; I actually enjoyed it. Once the test started, I stopped being nervous. There were twelve problems and we were supposed to do ten of them. I knew before it was half over that I wouldn't get through more than eight. I actually ran out of time a little over halfway through the eighth one. I've heard contradictory information about what it takes to pass, so I'm really not sure if I have a chance or not. I was reasonably confindent with what I turned in.

20:10

2005-08-01T20:09:00.000-06:00

My master's exam is on Friday.

11:33

2005-07-22T11:32:00.000-06:00

I've got a telephone job interview for a full time mathematics position at a community college next Wednesday at 15:00. This news is quite agreeable.

13:20

2005-07-20T13:19:00.000-06:00

I just uploaded my klein bottle icon to my blogger account. Not sure why I didn't think to do this before.

20:13

2005-07-17T20:12:00.000-06:00

I drew a map of the Near East on the whiteboard for the class today. I forgot my colored markers and couldn't do the water in blue, though. Last week they were asking about how far it is from Egypt to Israel and that kind of thing, so I drew up a rough map of the Exodus route. I thought my Mediterranean and Nile Delta were pretty good, although my Red Sea leaves something to be desired.

20:35

2005-07-15T20:34:00.000-06:00

I spent most of today helping David and Karen pack up their U-Haul. Seven other people were helping for varying amounts of time throughout the day, and they had professional piano movers come and move the piano. At around noon we had pizza and chocolate chip cookies. In addition to packing things up, they had some people come and look at the house, and were also discussing things with a realtor. Ideally, they would have sold the house by now, but they have to get moved in time for David to start his new job. Their son Darren will stay in the house until it sells; he has to find a place to stay, and I've suggested my apartment, since I'm planning to move out and Jeremy will need a roommate. Not sure if that will work out.

Continuing in reverse chronological order, my parents, who are on their way to a family reunion, stayed at my apartment last night. It was good to see them. My dad slept on the couch and my mom slept in the other bedroom.

Speaking of the other bedroom, I haven't mentioned my new part-time roommate. I have an aunt who is working on her doctoral degree, and taking classes here four days a week this summer. She's been staying at the apartment with me Monday through Thursday.

21:39

2005-07-13T21:35:00.000-06:00

I've been applying to a lot of jobs, and been turned down for a few. I only need to get hired by one.

14:02

2005-07-10T13:57:00.000-06:00

I forgot to mention there is no Ultimate Frisbee today, since they're doing a farewell party for a family that is moving away. This is just as well, since my legs are sore from Friday night and I don't feel like running.

13:46

2005-07-10T13:42:00.000-06:00

Today was the first lesson from Numbers. I thought Andrew was going to do it, but we managed not to connect with each other, or to get him connected with the notebook, due to a series of communication errors. First, I called Kyle and arranged to pick up the notebook from him at Greg's on Friday night. Then, Andrew called Kyle, found out I was going to do that, and figured I would bring the notebook to him once I got it (we live about three blocks apart). Then, Kyle forgot to bring the notebook to Greg's. Andrew was out of town on Saturday, and had been intending to prepare the lesson early Sunday morning. So he didn't answer his phone after I got the notebook Saturday afternoon.

Anyway, today was the first lesson in Numbers. The suggested chapters were 11 and 12, but we skimmed the ones before that and even read most of 9, which was about the first Passover celebration (after the one in Egypt). Chapter 11 is about manna and quail, while chapter 12 is about Aaron, Miriam, and leprosy. We talked about why it is wrong to complain against God, and the difference between complaining and asking for something. The kids were quick to say that we shouldn't complain because we shouldn't question God's plan, but one aspect they didn't think of right away is that our focus shouldn't be on current circumstances but on eternity. God never intended for the Israelites to be on a manna diet forever; the trip from Egypt to the promised land was probably just a few months. Instead of complaining about the journey, they ought to have been looking forward to the destination.

13:53

2005-07-09T13:49:00.000-06:00

Big day yesterday. I got new shoes, since the old ones were starting to fall apart. I got them at Fred Meyer for only $15 (60% of $25). Not bad. Later I got a chance to break them in. After making a few phone calls, I found out that there was no game night at Randy's this week, something I would probably have known if I'd been there last week. Instead, everyone was invited over to Greg's house. It was a large group; between fifteen and twenty people I think. Abe and I got there at about 19:30, at which point they were already in the middle of a game of kickball. The way they play, everyone rotates through all the positions, including "batter". We played that until everyone started getting tired and thirsty, then went inside for coolaid and nachos.

Greg's little brother Steve is the one who usually makes the coolaid. He likes to put in about four times the recommended amount of sugar. No one else will do this, but they like it so they let him make it. I watched him do this one time. First, he carefully measured the sugar in a measuring cup, except he did it heaping full instead of flat. Then he did it again (note that the first cupful fulfilled normal requirements). Then he decided there wasn't that much sugar left and just dumped the rest of the container in.

Once it started getting dark, we played a game called "pigstye". Basically it's a variation on dungeon tag. Two people are It. You don't have to actually touch someone to tag them, but just see them and call out their name. And, you don't have to touch someone to free them from the jail; you just have to wave at them, and have them wave back at you. Their next-door neighbors played with us, and we were able to use their yard so we had more space.

After it got really dark, we played three games of Capture the Flags. The teams were divided up randomly. For the first two games, the territory for each team was the combined front and back yards of one of the two houses, with the property line as the border. On flag was in a front yard, and the other was in the opposite back yard. Then for the third game, we put both the flags in the back yards, and made the front yards a "neutral zone" where no one could get tagged.

I spent most of my time in the first two games either sitting in jail, or harrassing border guards. In the third game, I was a jail guard, stationed in front of one of the back gates. That was exciting for the first fifteen minutes or so, when the other team was trying to come through that gate. At one point they ambushed me with two people, and managed to free a couple of prisoners and get away. I would have caught one of them if I hadn't been slowed down by a bush. At the same time, other members of their team came from the other side and tried to get our flag. They were all caught, and right after that we recaptured one of the prisoners who had been freed. The game slowed down after that. No one else tried to come through my gate, although I was still in a good position to survey both back yards and yell information to my teammates. The rest of the game mostly consisted of both sides patrolling the fence (which is less than waste high in places). Occasionally someone would vault it and try to do something. Finally someone on our team snuck around and ran in through one of the gates, grabbed their flag, and jumped the fence with it. I'm pretty sure that's the first time I've played Capture the Flags in seven or eight years.

23:39

2005-07-04T23:35:00.000-06:00

I have no idea how Sunday school went this week. Kyle and Andrew did it I assume, but I haven't talked to them yet. Mostly I've spent the week at the library, accompanied by my trusty algebra book.

Today we went to a Fourth of July potluck get-together that we've been invited to for the past few years. The family lives out in the country, and their friends and extended family all come for this, so there are a lot of people there. My old roommate Jeremy is in Portland right now, but his dad and three of his siblings are still in town and were there as well. Speaking of which, they were visiting Nichole over the weekend, and stayed at my apartment even though I was not there. They also picked up my mail for me.

They didn't set up the volleyball net this year, but we brought our croquet set and played a game. The course we set up was close to a traditional course since we wanted to keep it in a contained area. We ended up with six players: Me, my sister, Joel and Johnny (who are Jeremy's brothers), Amanda (whose house we were at) and Noah (who is Amanda's cousin or something). Now, Noah is about seven or eight years old. He is very small and doesn't look very threatening. He hadn't played croquet before, but was eager to learn. He was having some trouble swinging the mallet properly, so I tried to show him how, standing behind him and helping him position his hands. We hit the ball through one wicket together. Great. Then on the next one, I helped him get set up, then stood back a little to watch. I was leaning down to see the ball. He swung as if he were hitting a golf ball with a driver, missed the ball entirely, and hit me in the forehead with the mallet. I stopped trying to help him.

Since I didn't black out or see stars or anything, I figured it wasn't too bad. I held ice on it for a while just to be safe. There's a bruise, but nothing serious. Still, after receiving a blow to the head in the afternoon, it isn't necessarily the smartest idea to go watch a show involving bright lights and loud noises that night. I've got a bit of a headache, which I'm hoping will go away by morning. It isn't nearly as bad as the migraines I used to get, and it's getting better.

Speaking of fireworks, that display was impressive. As usual, someone had a radio tuned to the station where they have music choreographed with the explosions. Interestingly, for part of the time near the beginning they played the Star Wars theme. I kept expecting to see the Millenium Falcon fly in or something. Toward the end, the music stopped, and remained silent for the grand finale. Then, a few minutes after the finale, they set off six or seven more of them, as if they had forgotten those during the main show. Weird, but the show was still good.

I was thinking tonight that this would be a time when I particularly wouldn't want to be overseas. I remember when we went on a boat ride on the Sea of Galilee, they raised an American flag on the boat and played our national anthem. All of the students saluted the flag and sang along. This was maybe a week after 9/11, and we felt very patriotic and very homesick right about then. There was something about seeing the stars and stripes for the first time in weeks that really made me realize how far I was from home. I think that Independence Day is an especially good time to remember our soldiers who are stationed away from home, many of them in harm's way. If it were not for men like them, we would not enjoy the blessings of liberty.

"Oh thus be it ever, when free men shall stand
Between their loved homes, and the war's desolation!
Blessed with victory and peace, may this Heaven-rescued land
Praise the Power that hath made and preserved her a nation!
And conquer we must,
When our cause, it is just,
And this be our motto:
In God is our trust.
And the Star Spangled Banner in triumph shall wave
O'er the land of the free, and the home of the brave!"

16:20

2005-06-27T16:19:00.000-06:00

It seems I only make posts anymore about Sunday School lessons. Probably because that's about the only interesting part of my life right now. For yesterday's lesson, I actually combined two weeks' worth of material, because one of the lessons was too short and I wanted to cut some stuff out of the other one. So we talked about the inauguration of the priesthood, the death of Nadab and Abihu, and the Day of Atonement. In addition to Leviticus 16 about the Day of Atonement, I read out of Hebrews 9, which also had a nice review of the stuff we'd been covering about the tabernacle.

Next week (starting tomorrow actually) I'm going to be visiting my family for Independence day, and Andrew is going to be in Canada. As a result, neither of us is going to be able to do the class. However, I talked to Kyle on the phone earlier and he said he can cover for us. That lesson will be about Leviticus 19, and after that we start in Numbers.

In other news, I've applied for a job as a junior high / high school mathematics teacher at a small Christian school in northern Idaho. The application process reminded me of applying to TMC. Lots of information to gather and essays to compose, but I've got it all done now. Not much else to say about that at this point.