Five Six Signs There's a Paper Shortage in the Department

I mentioned before that the math department's paper budget is currently barely enough to cover printing tests for classes, let alone anything else. Here are some of the effects. And, yes, I've done all of these.

6. You raid the paper recycling bin for paper only used on one side.
5. You post everything to Moodle so that students can print it out on someone else's paper.
4. You start hoarding all abandoned papers and notebooks in classrooms.
3. You find an envelope on your desk and hoard it for scrap paper.
2. You look at the envelope and are pleased to note that if you unfold it, there is another blank writing surface on the other side.
And finally:

#1. You get junk mail in your mailbox and are ecstatic to see that one side of each page in the junk mail is blank.

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The Volt

Plug-in hybrids are a new class of car. You can't really describe their efficiency compared to a conventional gasoline-powered car using a single familiar figure. You could present energy efficiency in terms of a unit like "distance per kilojoule", but most people won't have a clue of what that means. The honest way to describe it is to say "Up to 40 miles without consuming gas, and then 50 miles per gallon". That's not so horribly difficult, now is it?

~MarkCC at Good Math, Bad Math

If and when Jean Luc gives out, I would strongly consider getting a hybrid. My current favorite pick is the Prius, but if the Volt or something like it were at a similar price, I'd certainly take a look. Last I heard, the Volt was going to be $40,000+, which is a wee bit out of my reach. Either way, it's nice to have accurate info on it. I wonder how much this little gem would up your home electricity bill...

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Fluttering

There's a series of math talks on Octonions this semester in the math department. The first one was yesterday afternoon. It dawned on me there that I do still have an interest in math for math's sake, particularly when it has interesting applications. Octonions turn out to be useful in string theory, which I found in a general hunt yesterday, and the Wikipedia article mentions special relativity and quantum logic as well.

It's also the first group I've come across that is neither commutative nor associative. Commutative means the order doesn't matter: 3*5 = 5*3, 6+8=8+6, etc. Subtraction and division by themselves are noncommutative, but since subtraction can be seen as adding a negative, and division is multiplying by the inverse, you can get around that. Matrices are the first things most people see where order really does matter. AB need not equal BA for two matrices A and B. Associativity means, roughly, that where you "put the parentheses" doesn't matter. So:

3(5*4) = (3*4)5

In the first case, I get 3 times 20, which is 60. In the second I get 12 times 5, which is still 60. Multiplication of real numbers is associative. In fact, I can't recall ever encountering a group operation that was not associative until reading up on the octonions.

The other thing I noticed at the talk was that, despite not taking any upper level math for the past several years, everything still made sense to me. Also I was a bit amused that the current grad students, who have all taken algebra more recently than I, didn't immediately recall that you generally use divisibility to establish that if a prime divides a product, it must divide at least one of the multiplicands of the product (Yes, multiplicand is a word; I just checked). The other nice thing about math is that I know the majority of people in the department and I might get away with not moving my office again, particularly since we've had several people retire and the temporary dean of Arts and Sciences (the bastard who sent out the gods-bedamned 'terminal' notices) is against hiring any more lecturers.

Still, I'm going to keep working through my old physics books. I wonder if it's possible to do a crossover math-physics doctorate here...

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Random Statistics

I just finished Season 3 of Lost (incidentally, does every season have to end on a cliffhanger?), and was poking around the Lostpedia, and came across this page. It counts the number of times Hugo Hurley says "Dude" in each episode. Now, this is his "stock phrase," but I'm not sure it would have occurred to me to count how often he uses it.

There's also a list of all the most frequently used catch-phrases. The one that I really noticed was "Don't tell me what I can't do!" It's most often said by Locke, but Jack's said it a few times, and I think there are a few others who have said it. Wait, Ben actually said that at some point in the third season. Of course, Ben seems to be an insane, megalomaniacal liar (emphasis on seems, since nothing is ever certain on this show).

As far as Lost goes, it's still amazingly well done. I didn't like Season 2 quite as well as Seasons 1 or 3, but all were quite enjoyable. I'm not sure how much of a hurry I'm in to get Season 4, simply because Season 5 won't be available until November (and Season 6, presumably, the November after that). Ah well.

Vaguely related note: Seeing Star Trek while in the middle of watching Lost made me notice some common features, presumably due to JJ Abrams' influence. First, he seems to have a soft spot for (or possibly mild obsession with) pregnancy; it's less obvious in Star Trek than in Lost, though. There was also a long, oddly lit corridor used in both works (on the ice planet in Star Trek, and at the medical station in Lost). Also, one thing that either Abrams or his writers does/do very well is to make the plot solidly work with the characters. With the massive ensemble cast in Lost, that's very important. With something like Star Trek, where fans know the characters already, it's arguably even more important.

Odd coincidence, I just realized: I started re-watching Buffy Season 4 just after finishing Lost Season 3. Strangely, Buffy 4 does not resolve any of the issues of Lost 3...

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Scientific?

I've started reading a book discussing probability theory: Chances Are: Adventures in Probability, by Kaplan and Kaplan. So far I'm enjoying it. It's intended as a lay introduction to probability, but I'd say the minimum pre-req thusfar is Math 108. That's not what inspired me to post.

Since they're discussing statistics, they bring up the question of testability, and what is a scientific question vs. a non-scientific question. Their example of a non-scientific question is, "Why is an apple sweet?" Er, sorry, but WHAT?!??!. I'm going to generously assume that they have no background whatsoever in biology or anything remotely related. In fact, that is a scientific question, and one to which I can think of several correct answer, depending on exactly what you mean.

If you mean, "What is it in the apple that makes it taste sweet?", then the answer is "sugars." If you're going a bit deeper and wonder what makes these things called sugars taste sweet, it gets more complicated, but the evolutionary answer is, roughly: "Sugar contains nutrients useful to mammals, thus it is advantageous for its taste to appeal to us. We describe this appeal as 'sweet'". Maybe you mean, "Why should an apple contain things that taste sweet to us?" Answer(1): We've bred and cross-bred apples over the years to give them an appealing taste. Answer(2): Having a taste that appeals to animals helps the apple's seeds propagate.

I think that, maybe, what the authors really mean is that "Why is an apple sweet?" is not a question that we can answer with numbers, and since numbers are the focus of the book, the question is not of interest to them. But to proclaim it's not scientific is pure nonsense. I'm trying to think of a non-scientific question that is not, well, just silly. Pretty much, as soon as you make a generic claim across any sort of class, you've made a scientific question. An exception might be: "Do all apple trees like the color blue?" or something equally bizarre. Even then, I can think of ways of testing it, and so that's still a scientific question, even if it's a strange one. So... "Are all apple trees in contact with an invisible dimension that we cannot detect in any way, shape or form?" Okay, that one's completely untestable by nature and hence unscientific.

Another way of creating a non-scientific question is to put it in terms of a particular circumstance or individual, particularly concerning something that happened in the past for which inadequate records exist. For example, I've hated boiled egg yolks for as long as I can remember. I love the whites, but I cannot stand the yolks. Why? I have no idea. I can tell you what I hate: the texture. I've tried getting over it, as it seems wasteful to throw away half the egg*, but as soon as I get more than a tiny amount of boiled yolk in my mouth, I want to throw up. Asking "Why does Qalmlea hate the texture of boiled egg yolks?" is not scientific because we have no good records of my reactions to food before I started remembering them. I can speculate that maybe I choked on something with a similar texture, or became ill, etc., but with no means to test that, it isn't a scientific question. We can make a general case that is scientific: "Do infants who experience negative reactions to a particular food retain an aversion to that food later in life?" That is something science can test and answer.

So there is one very simple way of reformulating their question to make it unscientific. "Why is this particular apple sweet?" If it's already been picked and we have no idea from which tree it came, this is not a question for science. If we do know which tree it came from, we can run tests on the tree to see if consistently produces sweet apples and even examine the chemistry involved. I suppose it's possible that this is the question they had in mind, but mathematicians should know better than to use poorly defined statements as counter examples.

Back to the book, I expect the Kaplans are paying blind homage to N.O.M.A. as it's sometimes formulated: "Science answers the how; religion answers the why." That's always seemed like a false dichotomy to me. Consider the case of the apple again. Apples that tasted sweet were more likely to be eaten by animals and have their seeds propagate further from the original tree, so sweet apples would have a better chance of producing offspring that produced more apples, which were more likely to be sweet, which were more likely to be eaten and have their seeds propagated far enough from the parent tree ... Why? Natural selection. How? Natural selection. I don't see a meaningful distinction between 'how' and 'why' in this instance.

*Now the cats get the yolks, so it bothers me less.

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Random Trivia

I played a game of Freecell for the first time in quite a while today, and then I remembered an old roommate telling me that every Freecell game was winnable. I wondered about this, and found that the claim is quite common, but not quite true. This site has the best summary of those I looked at.

First off, it is not the case that every possible deal of Freecell is winnable (first illustration at the link). However, it turns out that the game "only" produces about 32,000 deals (far less than the total number actually possible via random chance). Of those 32,000 deals, all but one is winnable: Game 11982. So every other deal that comes up on the Windows Freecell game is winnable.

Now I'm curious as to how many of the total possible deals are actually winnable... ^/^

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Easy Marks

I just finished grading half of the first set of Math025 exams (the version A ones). Usual types of errors, but one problem was SO bad that I almost wish I were the con artist type. Seriously. Problem states that the price with 5% tax was $106.25. What was the original price? Nearly every answer was LARGER than 106.25, some by several THOUSAND. Yikes. I mean, if nothing else, common sense should have told them something was wrong. So I'd like to sell them something that was worth, say, $100, then tell them that with sales tax it came to $1000. Not sure that many of them would know the difference. I think maybe one student actually got it right, and one was almost there (multiplied by 0.95 instead of dividing by 1.05), but the rest... I hope when they go shopping they have a math-guru along.

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Signs

There's a billboard advertisement for Cable internet in Idaho Falls. Nice BIG letters proclaim: "$29.95 per month!*" The * is clear at the bottom, and is completely illegible from the road. It seems like this ought to be illegal. Having seen their ad elsewhere, I know it's something like "*for the first 6 months."

Other news: my sword form is definitely improving. Don's corrections are getting pickier. For the non-practitioner, that means I've got the "choreography" down (mostly), but not all the fine nuances. Sort of like when you're sanding: you start off with a large grain to get off the roughest stuff, then progress to finer and finer grains. Well, I'm onto a finer grain sheet of sandpaper now. (I wonder if Don would appreciate being compared to sandpaper...? *shrugs*)

Not much else happening this week. We're looking at rational expressions in 025 (polynomials in fractions, basically), and ratios and rates in 015, and we're having a test over Fibonacci numbers and exponential/linear growth in 123. I decided to cover the growth stuff rather than Fractals mainly because there's more stuff there that they will actually use (interest calculations come to mind). We did take a tiny look at fractals, in the form of the Koch Snowflake and the Sierpinski Gasket. With the Koch Snowflake, you draw a triangle, then put another triangle in the center of each edge (should trisect the edge). Now you have 6 triangular points, and put a triangle on each of their edges. Now you have 12 points.... and keep going. The end result does look somewhat like a Snowflake.

The Sierpinski Gasket is similar, but opposite in the sense that you remove things rather than add them. Start with a shaded triangle. Find the midpoint of each edge and draw another triangle connecting those points. Erase the shading inside the "new" triangle. Now you have three shaded triangles inside your original. Find the midpoints of each side, connect them into triangles, and erase the shading. Now you have nine shaded triangles... Repeat ad infinitum.

There's a cool variation of the Sierpinski Gasket that gets to the same end shape through random processes. We didn't get to that in class, but I thought it was fascinating.

But now I suppose I ought to write said test, so that they can take it tomorrow night.

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Improbable Vest-Making

Question from the most recent Math 015 exam: "It takes 3 1/4 hours to make a single beaded vest. There are 52 working hours. How many vests can be made in this time?"

Correct answer is to divide 52 by 3 1/4 --> 52/(13/4) = 52*(4/13) = 16 vests.

Many got this answer or something close to it. Several came up with 169 vests (by multiplying rather than dividing). One person came up with a number over 700. Let's see, it takes more than 3 hours to make a vest, and you're going to make 700 of them in 52 hours? I'd like to see your time machine!

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Pain. Head. Tired.

I'm not quite as incoherent as that title sounds, but I've had a screaming headache nearly all day. Taiji helped some. I'm wondering if it's caffeine withdrawal, actually...except that I don't think I've gotten myself addicted to caffeine again. It's that kind of headache, though. So if it's not a withdrawal headache, I must have one heckuva cold coming on. *sighs*

I'd be in bed by now, except I promised my 015 classes I'd bring their current averages tomorrow when they take their test. Which meant I had to get grades entered in and averaged out. It's easier with my Pocatello classes, since grades get entered in as soon as I get the grading done. My IF classes, I tend to grade in the half hour before class and I just write them in my notebook. But they're in, now.

We didn't do much in Math 123 tonight. I had hoped to let them go waaaay early, but they had lots of questions about two sections of homework (they REALLY don't like the golden mean or the quadratic formula: which means they definitely need to spend more time with them ;^). Then I realized that we still had a bit of Chapter 9 to go, so we looked at gnomons and similar shapes. We'd done rectangles already, but not triangles or rings. But there was nothing really new tonight; just a chance to recoup and review. I haven't decided if I'll do any of Chapters 10 or 11 yet, or if I'll just move on to 12... Chapter 10 has linear and exponential growth, which is important. Chapter 11 doesn't really interest me that much, so far (symmetries...the tiling stuff is cool, but I would like to understand it better before teaching it). Chapter 12 is Mandelbrot stuff.

Okay. Sleep now.

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Strange Day

I had a Matrix test today. My version of studying was to work on the homework that is currently late (close to being done now) and look over the Polynomial Matrix division algorithm in the book (which I couldn't follow, but I figured out my own way that seems to work), since there hadn't been any problems over it. I concluded that such a problem was likely too long for the test, unless the polynomials were of degree two or less.

I had no clue how I'd do on the test, but I think I did all right. There were 10 problems, and we needed to work 8. I got seven of them done... One of the remaining three was about elementary forms of polynomial matrices, which I had essentially ignored. One was three canonical forms for one matrix... I could think of two (Row-Column equivalence and RREF)... Possibly Diagonalizing it would have counted, but I wasn't sure. The last one was to prove that an eigenvalue of (A+B) must be a sum of the eigenvalues of A & B. I tried many things, and kept getting stuck. Then I reread the instructions: Prove or Disprove. I picked two random matrices, tried it, and NOPE. Not true. So that got me up to 8 problems, and I was done.

The others were mostly straight forward, since I had mostly finished the homework.

Then I was starved and couldn't breathe (and it was after 16:00 so I was already late to help with Melissa's taiji class), so I made a run home for decongestant and food. While I was there, my mom called. Grandma's in the hospital again. She fell on Tuesday (and was stuck till Mom got home; I wonder if she'd accept an emergency notification device if I bought one for her...) and today when she went to Dialysis, they decided she'd probably injured something in the fall. So they sent her up to the hospital for something that sounded like "pistogram" or "pistulegram" or something like that. Mom thought they might be done by 19:00, but wasn't sure. To be honest, I think Grandma would be better off in the hospital at the moment. She's been off all week, and 'round the clock observation would be a very good thing. So I was more relieved than worried to hear she was in the hospital again. *sighs*

Last night I stopped over at Grandma's house after work, and Grandma was already in bed. Mom said Grandma wanted some support handles put in on one of the upstairs toilets, so I helped figure out how to put the thing together. We're not sure why she wanted handles on that toilet, since it's no closer to her room than the main bathroom, and it's smaller, so harder to get her walker in there, but the handles are on now.

No time for writing since Sunday, mainly because of writing and grading tests. One more to write for next week, and I have 015 tests to grade, but those tend to go quickly. I do need to get Math 123 homework graded this weekend, before their test, but that's doable. There are less than 20 people in that class.

Random connection: I've got the first draft of next fall's schedule now. It's a nice schedule, actually. I work MW evenings, two classes, and TTh from 9 am to 14:15 (with a break in the middle). Which leaves Fridays free (except for the new Math025 testing center, possibly), and most of MW free. I like this. I've got one section of Stats, so I'm hoping to restructure my teaching style there. I was getting so bogged down in HW grading last fall (partly because of Grandma being in and out of the hospital, but still, not good). I also have one that I haven't taught: 257, which is apparently a math class for elementary ed majors. Annik says it's fairly interesting (except she's done it 6 semesters in a row and is now sick of it).

Background Noise: Ahsan and Dina seem to be having a major fight in her office. It's quite distracting, and loud enough to be heard despite her door being shut. I'm not sure that shutting my door would help any.

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Just Rambling

Forgot to mention that, yes, dry erase markers do work bettr than chalk for the graph theory stuff. So far. It's easier to erase cleanly while trying to find paths through a complicated graph, at the very least, and the colors show up better. We're about done with Chapter 5 (I've got a few more examples to do), so I don't know for sure if the same will be true through the rest of this section of the book.

Taiji yesterday was quite enjoyable. I've found that my push-hands is better against James than it is against Mark or Joe. Why? Because James is much larger than I am and has a good root. This means that I absolutely cannot get away with trying to muscle him (and if he were better, I would REALLY regret trying to muscle him), so it has to come from the waist and my own root. Mark and I are about evenly matched, size for size and weight for weight. He's slightly larger than I am, but overall it's an even match. Joe is much more slender than the rest of us, which makes it a horrible temptation to use muscle. However, he's good enough to use any arm tension I give him. It just hasn't broken me of the habit yet. *sighs* Oh, and Don offered some sword lessons since I'm in IF two extra days a week. So I've got a sword lesson on Wednesday. That should be fun.

Other news... Grandma. She gets better sometimes, and then she gets worse, and better, than worse, but the getting worse is winning out. I don't think she's going to last much longer. I don't know if she WANTS to last much longer, as tired and miserable as she's been lately. I'll miss her when she goes. Strangely, the thing that bothers me the most is that, if I ever have children, they won't know their great-grandma. I guess that's an odd thing to regret.

Her friends in Akron are the same chronological age she is, but they look oh so much younger than she does. She's starting to look like I remember Great Granmda Fern looking (and I'm not about to tell her that; I doubt she'd appreciate it). Grandma Fern lived to be 90. She died on Monday, 13 February, 1989. I remember her being hard of hearing and moving slowly, but I don't remember her ever having as many problems as Grandma Parker is right now. I suppose the reason she's so much worse off is her diabetes. She's been diabetic since she was 10. They told her mother (my Grandma Fern) that she probably wouldn't make it to 30, let alone past 70. She's had a good, full life. I do wish she'd gotten to see her friends from Akron more often after she moved up here.

My Grandad Parker died when I was a junior in high school. He was a gruff, hard-to-like man who teased me mercilessly as a child (and not in a way that I enjoyed), but he truly loved my grandma. Details are fuzzy, but I remember an incident where he thought Grandma had been hurt, and I heard him calling for my mom to come and help. The pain and fear in his voice told me everything I needed to know about him. Hard and gruff as he was on the outside, he was a good man inside.

*sighs* This went further afield than I'd intended.

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Paths

Let's see... feeling much better this week. The hunger has died down considerably. I'm starting to wonder if (before I knew I was gluten intolerant), there was permanent damage done that makes it more difficult for me to absorb nutrients. As I no longer have symptoms (since I now avoid gluten-containing foods), I had assumed not, but the damage may be subtle enough that it doesn't show up unless I don't get enough of whatever nutrients aren't being absorbed. *shrugs* Short version: multivitamins are my friend.

I skipped out on about three eighths of my math lab duty today. Why? Because I realized I had forgotten both my Matrix notebook and my taiji pants (my nicer pants are slightly too tight for taiji). If it had been only one forgotten item, I wouldn't have gone back for it, but for two... I lucked out and got a closer parking spot when I got back, though.

We start a new chapter in Math in Modern Society today. Euler circuits = graph theory. This looks to be lots of fun to teach. :^D Also, I finally remembered to bring in some dry erase markers and an eraser; I'm in the classroom with one dry erase section of board (put in for a faculty member who's allergic to chalk). I expect that this will be better for drawing the paths, etc., than the chalk will. I'll find out this evening.

Last but not least, Kim is proving quite enjoyable. Currently, he's found his "red bull on a green field" and is plotting escape. I am nearly convinced that this book was part of the inspiration for Terry Pratchett's The Colour of Magic, where Rincewind guides the first ever tourist, Twoflower. There's a similar...flavor between the two. Other than two unlikely characters journeying together, though, the plots have little in common.

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