Ants On A Box

Two and a half years ago, I worked for a teaching program at Queen's that could help first year calculus students get extra marks. It was called Math Investigations and its purpose was to show interesting problems that students might not see in a regular class. As a third year math student, I could solve most of them in a brief sitting but one problem called "two ants" eluded us and it just happened to be the first problem we presented.

The initial setup showing where the ants are.
My partner for TA'ing that section was James McLean and we were later joined by Rob Wang. We downloaded problem sets picked out by the head of the program - Peter Taylor - and he also happens to list the ant problem first. The premise is that a 12x12x30 box houses a male ant and a female ant and they are located on the square ends. One is eleven twelfths of the way between the floor and the ceiling, the other is eleven twelfths of the way between the ceiling and the floor. One ant wants to meet the other by crawling on the surface of the box - taking the shortest possible path. If you read the solution we were given, you will see that it does not prove which path is the shortest or give a real indication of how one might do so.

Very Poor Choice Of Words

Sorry that the site was down for over a month - my host was being bullied by his ISP. But now that the problem is over, I will make the post that I would've made at the end of March - about a protest that I tried to organize. Right now I am at the University of British Columbia and I live on campus in a residence called Marine Drive. I have quite enjoyed this place: the buildings are new, there aren't any first years around and for this particular building, I don't have to move out at the end of the year - I can keep staying as long as I keep paying. The rent includes all the necessities like a network connection which is very fast and has unlimited bandwidth (thanks to MAC address spoofing). So it would be a good idea for me to keep paying rent.

Logos for Rent and its censored version.

At the end of March, people in my residence and other residences put on a production of Rent. Close to the date of the performance, I was disappointed to see that the musical would in fact be the school edition. The program included the fine print: "With the permission of the Jonathan Larson Estate, this version of RENT has been adapted for use in schools and other producing organizations. While retaining the dramatic intent of this groundbreaking musical, minimal changes have been made to language and one song ["Contact"] has been deleted." They say that the changes are minimal. My ass. But the biggest lie they tell is that their censored musical retains the dramatic intent of the late Jonathan Larson. He died before the school edition existed and yet MTI presumes to know what his opinion of it would be. Did Larson just decide to put drug references in the script for the hell of it? Because he didn't think they were important to the show? I highly doubt it. You are either being true to an artist's vision or you're not.

It was frustrating to see that a university would be putting on this version of Rent even though it was designed for high schools. I think UBC should be more like Hollywood High School which performed the full version of Rent in 2010. The Wikipedia article says it was the first high school to do so - I am amazed it took this much time for one to act sensibly. However, I suspect that UBC's decision to use the school edition was made for financial reasons. It costs less to license the school edition - something else that bothers me because it has a chilling effect on the feasibility of performing the real show. I take some solace in the fact that the version performed was somewhere in between Rent: School Edition and Rent. The cast restored the swearing and other things, so I think they reverted the changes whenever it was easy to do so. The word "fuck" does not appear in the school edition but it was definitely in the play I saw. I was actually surprised to see that the full script only includes it six times because it seemed like I was hearing it a lot more. Anyway, everyone in the production was wonderful so this is not what I felt I had to do something about.

Mispronunciation

Happy leap-day to anyone reading this! How often does a leap-year occur? It is not once every 4 years anymore. It is more like 97 times every 400 years! Adding a day once every 4 years would be correct if the year was 365.25 days long. This is what the Julian calendar did. But then it was discovered that a year is more like 365.2425 days which led to the Gregorian calendar. I like the story of how this was implemented. Centuries of not accounting for this difference caused a 10 day discrepancy between the night sky of 4 October 1582 and the night sky of 4 October in the year that the Julian calendar started. Therefore Pope Gregory XII pronounced that the next day would be 15 October 1582 making the month have 21 days.

The system now is to add an extra day to years that are divisible by 400 and to years that are divisible by 4 but not 100. This means that while the year 2000 was a leap-year, the year 2100 will not be. My prediction is that at least a few printed calendars will be incorrect in the year 2100.

Anyway, what I actually want to talk about is a series of Pronunciation Manual videos on YouTube. The channel parodies instructional language videos by telling you the worst possible way to pronounce something. The meme started in April 2011, I think as a way to take advantage of video monetization. It is stupid simple to make a PronunciationManual video. Each one is 8 seconds long and just consists of a printed word with a voice over.

A New Lease On Life For The Matrix Phone

The only mobile phone that I have ever owned is the Samsung SPH-N270. In 2003, when The Matrix Reloaded came out, 2500 of these phones were made and sold for $500 each to promote the movie. Mine is number 551. They were by no means the most feature-rich phones of their day but they may have been the coolest. Few phones are able to divide a community in this way. Everyone who knows about the N270 either thinks it is the ugliest phone ever or the sexiest phone ever. My opinion is obviously the latter.

The only carrier participating in the promotion was the American network Sprint PCS. Figuring out how to use the phone in Canada was a minor hurdle to overcome, but that is nothing compared to the hoops I had to go through to get this phone fixed. The phone is now 8 years old which is probably twice the average lifespan of a cell phone. The only forum posts about the phone that I have seen recently say something like "I used to use my Samsung N270 but now either the phone or the battery is broken." This happened to me but to make a long story short I found a company that is willing and able to do internal repairs on this phone and other phones from that era. That company is CellFix and they did an amazing job.

While I was stuck with a broken cell phone, I briefly considered doing what normal people do and purchasing something more modern (like an Android phone). But now that it is clear that my matrix phone is still usable, I will proudly recount my experiences with this phone and mention some tips to anyone who has one or wants one. It's not like I will stop using it any time soon!

The matrix phone on my desk.

Messing With Ill-Defined Physics

What's a fun thing to do when you learn a less than intuitive concept? Searching the web to find another person's opinion of it! I recently learned about Grassman numbers and my search turned up a blog post by a professor named Luboš Motl who makes some pretty debatable claims. After reading the post, I found out that he is actually quite famous. So yes, he probably knows much more than me about the subject, but I must still object to how complacent he is with using an object and not defining it.

Reverse Engineering Star Wars Music

First of all, happy holidays to anyone reading this! You didn't think I was going to let Christmas / Grav-mass go by without a post did you? Well I absolutely would have if I didn't have this post ready in time. Spreading the spirit of the season can be done in a small number of words - and all of the posts I write have to be long. No exceptions!

Anyway, like many people who have a piano at home, I sometimes hear a great piece of orchestral music in a movie and try to play an approximation to it on the piano. Usually what I try to play is full of mistakes and I lose interest after half an hour. However, my approximations to two Star Wars songs have evolved into fairly well defined pieces that I can play from start to finish. Want to guess which ones?

The first measure of music that plays for a set of Star Wars end credits.

Both pieces are ending themes so they have to merge into this music that plays during the black and blue credits of every Star Wars movie. That should narrow it down significantly. Anyway, in the rest of this post you can find audio files and sheet music. Learning to play this was satisfying enough. But then I realized that this was a perfect opportunity to learn the music TeX packages so it's a win-win situation.

Those Physicists And Their "Physics Proofs"

There are plenty of cases where a proof written down by a physicist is worse than a proof written down by a mathematician, but this is a particularly bad one. In one of my courses, we got to derive the Dirac matrices, which are instrumental in describing spin 1/2 particles. These four matrices are written as $ \gamma $ with an index. One definition of them says that they should satisfy the anti-commutation relations of the Clifford algebra:

\[  \left \{ \gamma^{\mu}, \gamma^{\nu} \right \} \equiv \gamma^{\mu}\gamma^{\nu} + \gamma^{\nu}\gamma^{\mu} = 2 \eta^{\mu\nu} I  \]

where $ \eta $ is the Minkowski metric from special relativity.

\[  \eta = \left [ \begin{tabular}{cccc} 1 & 0 & 0 & 0 \\ 0 & -1 & 0 & 0 \\ 0 & 0 & -1 & 0 \\ 0 & 0 & 0 & -1 \end{tabular} \right ]  \]

How big do our matrices have to be in order to satisfy this? They obviously cannot be 1x1 matrices because these are just numbers that commute. It turns out that they have to be at least 4x4 but all published sources I have seen fail at explaining why. I will go through the physics proof that is often given and then set the record straight by writing a real proof. If it appears nowhere else, let it appear here!

So Now The Meaning Of Life Is 137?

Normally when I see an article about numerology, astrology or homoeopathy, I don't give it the time of day. But this one is interesting because it sounds like the author actually made an honest effort to read up on the science related to the fine structure constant and just got it horribly wrong.

The article is The Mystery of 137 and it lives on a site dedicated to the new age philosopher Ken Wilber. Who would've guessed that a site like that would actually have a correct equation that comes up all the time in quantum electrodynamics?

\[ \alpha = \frac{e^2}{4\pi \epsilon_0 \hbar c} \approx \frac{1}{137.036} \]

Yo Dawg, I Heard You Like Guns...

Awhile ago, my friend showed me Pimp My Gun. This site has a Flash driven app that lets you assemble the weapon of your dreams. It is basically a drawing program that has a library of hundreds of firearm components. There is so much room for customization. I tried it out and came up with the following guns:

So we sent a gun salesman to your mother's house, so you can nag mum to buy a magnum!

Jungle camouflaged AUG

Stupid Math Questions

I never turn down a chance to be a smart-ass. One of the best things higher mathematics can teach you is how to go back and correct almost everyone who claimed to be teaching you math. It's almost impossible to a cover a decent amount of material in a math course without sacrificing correctness. This is true in grade school when you learn tons of stuff that isn't real math and it is true in grad school when writing one proof that is perfectly rigorous takes two weeks. Here are some common questions that need to be rephrased before they make any sense. The links point to where I found the questions but they could've come from anywhere. If they look like they were taken straight out of your high school calculus textbook, they probably were.

Stupid

Original version of question 1

Smart

Better version of question 1

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