Bands, Blue Men, Bridges, and Balls of Toilet Paper

A lot of stuff has happened since I last wrote here, so this post will be an interestingly funky hodgepodge of stuff (hopefully).

First up: I just got back from an end of charity gig I was playing at with the engineering jazz band. It was pretty rocking, if I do say so myself. I'm also listening to a Blue Man Group CD while writing this, so I'm definitely riding on a bit of a music high at the moment. The Blue Man Group album (The Complex) is also really good, so I'm not really paying attention to what I'm writing. I apologize for this.

Second: The final project of my Mechanics of Deformable Solids course (which shall be referred to henceforth as 'MoDS') was to build a bridge out of cardboard (well, millboard, technically). We tested the bridges this week, which was a lot of fun because (a) it helped satisfy everyone's natural need for watching things break, (b) some of the failure's were pretty cool examples of shear deformation as the bridges slowly contorted around weak points, and (c) my group did well, supporting five hundred pounds with our 0.96 kg bridge bridge and getting within ten pounds of our predicted failure load. Granted a 1:250 weight to strength ratio is not unbelievable, as there was a group that supported over seven hundred pounds (and the all time record is rumoured to be over a thousand), but it's always nice to see stuff work the way you expect it to.

And last up: the balls of toilet paper. Yes sir. This one needs some explaining...

You see, on the day of the bridge testing, it also happened to be April Fool's Day and naturally, in our houseful of engineers we wished to celebrate the occasion. Naturally, with a Costco-sized supply of toilet paper available, the thought of strewing paper around ('TP'-ing) one of housemate's rooms was suggested, but, nice people that we are, we decided that was too messy / unoriginal / difficult to clean up. Then the classic idea of gluing all his furniture to the ceiling (using glue leftover from the bridge project) was floated -- again though, too evil.

Then genius struck.

We'd leave the toilet paper rolls in their plastic packaging and tape them, and other small items lying around, to the walls and ceiling. It was simple, clean, surreal, visually interesting, and (at least in our own eyes) a work of art.

You wouldn't think that this plan would be very hard to carry out for a couple of guys who just built a bridge a gorilla could walk over out of cardboard... but it turns out that scotch tape doesn't adhere well to the ceiling and it was having a lot trouble supporting the weight of the toilet paper rolls. The prank was turning out to be on us as the few rolls that were able to briefly stick to the ceiling came pelting down onto our heads after a few minutes. Lesson learned: use masking tape; it's much more effective.

So finally all the toilet was stuck up, with a water bottle and kleenex box strung up for good measure, and we built a little pyramid out of the remaining toilet paper and rubber ducks to fit in the doorway. The whole thing went over with my other housemate pretty well, although we quickly discovered that toilet paper balls made good projectile weapons in the same way that nerf balls do (because they have enough weight to be tossed, yet still don't hurt). After this discovery, we spent a bit more time exploring the possibilities it created (read: all out toilet paper warfare) before cleaning things up (all right, technically, we haven't gotten to the cleaning part yet).

I could go on, but I'd rather go and sing along to some songs on my computer.

If I sing a song / Will you sing along / Well I keep on singing right here by myself... ba dow dow dow bow dow dow dow, ba dow dow dow ba dow...

[Edit: For anyone concerned that with all the above shenanigans, I'm not studying / writing about studying enough, let me add that as of last Tuesday, my last 'midterm' was over, and as of Friday classes are done for the term. So yes, much studying will ensue over the next month as exams hit, but that won't stop us from having our exams and toilet paper too.]

How to Buy an Airline Ticket

Well, I can finally say I've attended an MIT lecture. Dr. Belobaba from MIT's International Center for Air Transportation (ICAT) dropped by today to give a guest lecture on the topic of airline pricing schemes and revenue management.

It was an interesting talk that did a good job of explaining why airlines feel the need to have multiple fares for the same flight and to sell tickets at different prices depending on when they're bought.

Basically, airlines want to sell as many high-priced tickets as possible, but they know that there are a lot of people who will only fly at lower costs, hence the need for differential pricing. Then of course, the people who were willing to pay more won't be quite as happy to part with their money if they know that someone else is getting the same service for the same price, which is why airlines introduced restrictions on low fare tickets including "Saturday night stay" conditions that prevent the type of quick round-trips that businesses require.

But on top of these differential pricing schemes, the airlines also use revenue management. That is, they reserve a certain number of the more expensive tickets based on statistical models for how many they believe they'll be able to sell. This is sensible enough, because if they know that they will eventually sell out a given number number of expensive tickets, they don't want those seats going to starving students who will only pay the cheap rate. Of course, they don't know how many tickets they'll be able to sell exactly, so that's where the probability comes in.

Technically, you look at the expected value of some probability function to do this, but all that means is that the cutoff for reserving a ticket of a certain class is the point at which you get the same number by multiplying the ticket's price by its probability of being sold as you do when you multiply the price of a cheaper ticket by its probability of being sold.

Anyway, what this all boils down to is that, first of all, you won't get the super cheap tickets months in advance, regardless of the probabilities, because airlines know they'll be able to unload those later relatively easily. The cheap tickets actually start appearing once the revenue management system kicks in and it realizes that the expensive tickets are being undersold. Now, if the expensive tickets are actually selling really well than you can forget about the cheap ticket and start wishing you had bought one before the prices tripled, however the upshot of all this is that given the statistical anomaly that is the current economy the model forecasts might be overshooting slightly.

I'm Stupidly Full Right Now

As I mentioned in my last post, I was making pork chops for dinner. The grainy picture above, taken by my cell phone, shows the results. It was quite good and the actual cooking is really student friendly (it only has something like four ingredients) so I can officially recommend the recipe.

Rainy Day

It's Saturday evening and it's been raining all day. That's not really a bad thing; I've gotten some work and laundry done and a pair of pork chops are currently being simmered on the stove, so all in all it's been a decent Saturday.

If I Wrote a Textbook...

Godzilla's foot is towering 0.3m above Billy's head. If Godzilla's foot weighs 200 kg and Godzilla's leg muscles exert a force F_A of 30 Newtons onto the foot acting downwards at an angle of 30 degrees to the horizontal ground plane (see diagram), how much time does Billy have to move to avoid being flattened?

See now this is the type of problem people can relate to.

[Bonus: Write a differential equation expressing a werewolf's rate of change with respect to the phase of the moon. Use this equation to calculate how quickly someone needs to be locked in a cage once they start transforming, given that signs of werewolf behavior are detectable after the transformation is 20 percent complete. Use a safety factor of 1.2 and assume the lock is sturdy.]

EDIT: A few corrections for the first problem: assume that Godzilla's foot is large enough that it's horizontal motion in the brief time before impact can be neglected and that the foot will indeed impact Billy if he does not move. Furthermore, assume the foot has no velocity at the instant depicted in the question. Resolution of ambiguities in the bonus question are left as an exercise to the student, but be sure to state all assumptions and reasoning.

Lots of Mayo

The above picture was of my brunch today. It's a tuna salad bagel plus some deviled eggs. I know it doesn't look particularly fancy, and compared to the stuff my housemates make (oven roasts cooked with wine, homemade chili, etc.) it's not that adventurous. However, I've had a bit of a phobia with hard-boiling eggs ever since I saw one of my previous roommates attempt it to disastrous results (yolk... everywhere...), so this is a something of a breakthrough for me. Also, it tasted delicious.

Ah, student cooking. Now if you'll excuse me, I need to go cook up some noodles for lunch tomorrow (we ran out of bread).

Crazy Random Happenstances

So I went on the band trip I was mentioning earlier. It was a good ol' time, going to a rival engineering school and playing with their band. I'll have that Maniac song stuck in my head for a while now.

You may also have recognized the phrase "crazy random happenstance" used in the title of this post as a line from the musical Dr. Horrible's Sing-Along Blog. It's hard to describe how cool this online musical really is -- I mean yes, it has an amazing cast, writers, and songs (many of which were recently blatantly stolen and rewritten for the university's Faculty, Alumni, Staff, and Students [FASS] Musical) -- but more than that, the DVD version has a musical commentary track. The awesomeness of this is mind blowing. Go grab some popcorn and have a listen!