The Life of a Mathematician

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.

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.

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."

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.

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

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

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.

11:2*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.