I wonder sometimes: if pi could think, what would it think about all of those silly humans who celebrate Pi Day every year? Would be honored? Or offended? Given that every Pi Day makes me feel old, how does feel about the aging process?

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2013 starts a sequence of years with interesting factorizations — factorizations with all primes less than 100. These are numbers for which it is easy to write interesting problems, and the next few years should give plenty of those.

In other news, 2013 is the first year since 1987 consisting of four distinct digits. It’s also the first new year we’ve entered since a whole year ago… and that’s a cause for celebration, and possibly alarm and concern.

Have more trivia about 2013? Please comment and let me know!

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In the 1700s, people were interested the solving the “Longitude Problem”: how does a sailor determine his longitude? Without a good solution, sailors lacked good position data, which could lead to shipwrecks. It turns out that the Longitude Problem is equivalent to determining local time, and one solution was to build accurate and portable clocks.

These issues of longitude and time are fun to think about, but I noticed that they require making a lot of non-canonical choices. Here, by *canonical* I mean choices that are natural or motivated; *non-canonical* choices are

arbitrary and would make just as much sense if chosen any other way.

Consider this: There is a (reasonably) canonical place to set 0 degrees latitude; it is natural to define it as the equator, being halfway between the poles and splitting the globe into equal halves. But as there is no “east pole” or “west pole”, there’s no such natural choice for 0 degrees longitude. We currently use the Greenwich meridian as 0 degrees, but there’s no good reason (besides history and random chance) that Greenwich should be special… in fact, the French used the competing Paris meridian for some time. The way we define longitude on the globe is completely arbitrary, and we could just as well use a Svalbard meridian instead.

The measurement of time is similarly non-canonical. Each civilization in history has come up with their own calendar, with its own quirks. The calendar that we use today is just one of those, and there’s no clear reason that it is naturally better than the others. In the end, the everyday world that feels so natural to us is actually based on an accumulation of historical coincidences.

While we’re discussing non-canonical choices, I’ll quickly list a few more that I noticed recently:

- Cars drive on the left or right depending on where you are in the world.
- The UK has 20 pence coins while the US has 25 cent coins.
- In some parts of the world, floors of a building are numbered starting at 1, while in others, floors are numbered starting at 0.
- Electricity might come in 110V or 240V varieties, with numerous different outlet types.

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One piece of data that I find interesting is sleep. The amount of sleep that I get each night strongly affects how happy and productive I am, and I want to analyze this data to see if there is anything that I can learn about my sleep patterns. So I’ve been recording my nightly sleep schedule — when I go to sleep and when I wake up. The hope is that I can eventually produce pretty graphs of when I sleep. It pains me to think that some people could be recording their sleep schedules too, but instead fail to do so out of laziness.

I’ve been recording sleep data since 13 March 2012 (excluding naps, e.g. boring classes; all times approximate and rounded to the nearest five minutes), and I can already see some patterns. The full analysis hasn’t happened yet (I plan to wait until I have more data), but here’s some preliminary statistics (as of today, August 26).

*Average since March 13: 7:59:21
Maximum: 12:29 on March 29
Minimum: 0:00 on March 24 (thanks to red-eye flight)
Minimum positive time: 2:45 on June 3 (thanks to ARML)
Standard Deviation: 1:27:08*

I think I’ve been sleeping more (and more normally!) over the summer:

*7-Day Average: 8:41:25
15-Day Average: 8:39:20
30-Day Average: 8:29:52*

Let’s hope that this trend continues!

There have been a couple of erratic weeks:

*Maximal 7-Day Standard Deviation: 4:14:15 (week ending March 30)*

And some very regular weeks:

*Minimal 7-Day Stanford Deviation: 0:04:30 (week ending April 15, a week of times between 8:00:00 and 8:10:00)*

Conveniently, recording sleep data also makes me realize when I’m not sleeping enough and motivates me to sleep more. Which is a good thing.

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I got two computers in the mail this week!

The first computer is an old Lenovo Thinkcentre that was acquired from eBay. It’s going to be the Stanford University Mathematical Organization‘s new server. We’ll use it to do a whole bunch of things, including but not limited to a number of jobs for the Stanford Math Tournament (registration, grading, and tons of data analysis). I installed Debian Squeeze last night, and it should be fully functioning within the next few days.

The second computer is a Raspberry Pi! I ordered a Raspberry Pi from RS on June 29, and after increasing amounts of frustration, cancelled that order and ordered again from Newark on July 20. After another few weeks of waiting, it’s finally here! It looks really pretty. Unfortunately, I’m still lacking various cables, an SD card, and free time, so I can’t play with it yet. With everything else that I should do this week, that’s probably a good thing. I’m still trying to decide what to do with my Raspberry Pi. Any cool ideas? Let me know!

Before I got my Raspberry Pi, I had heard that it was credit-card-sized, but I was still surprised to see how small it is. It’s amazing that something that small could have so much computing power — this computer is more powerful than the best supercomputers from only a few decades ago.

Here’s a picture of the two computers:

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Coincidentally, 6 and 28 are both perfect numbers, so I declare today to be Perfect Number Day. This all goes to show the deep connection that has with perfection. Or maybe it just demonstrates that sufficient numerology can be made to prove anything.

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As for results, SFBA’s teams did amazingly well: A1 and A2 were 3rd and 7th nationally, the first time that any organization has had two teams in the top 7 at ARML. Next year, we’re aiming for 1st and 2nd on the national scoreboard.

Some random thoughts from ARML:

- Tie-dye was an amazing shirt color. Pink was pretty cool too.
- I should try to avoid losing my bed next time.
- Flip, Flop, Fliegerspiel
- Bif! Bif! Bif!
- I am Chen!
- Yee!

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Here’s a movie named after this most wondrous number: Pi.

Disclaimer: I am not responsible for any mental harm resulting from viewing this movie. You have been warned.

The movie can be entertaining, but it is also somewhat disturbing. The mathematical inaccuracies are also rather unfortunate.

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- have the same number of primes in their prime factorizations (counting multiplicities). The smallest numbers such that have the same number of primes in their prime factorizations are , so this is actually fairly rare.

And some more really rare properties:

- 2012 is not odd.
- 2012 is not prime.
- 2012 is not a square.
- 2012 is not squarefree.
- 2012 is not a perfect number.

I know I haven’t posted much recently. It’s a poor excuse, but I’ve been busy. I do have a number of things that I want to write about, however, and I’ll get to them eventually.

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I didn’t know much knot theory and hadn’t ever seen a formal development of non-Euclidean geometry, so I learned some things this summer. I stayed barely ahead of the classes (and probably wasn’t as helpful with homework as I would have liked), but having seen each of these subjects before, I was able to say broad generalities about big ideas. I appreciated knot theory more than non-Euclidean geometry. The knots course was a course in waving your hands and playing with rope, and I found that much more enjoyable than the formalism of the geometry course.

What should be the ultimate goal of a short math course at a summer camp? Any material that is taught will probably dissipate fairly rapidly; assuming their memory is like mine, I would be surprised if any of the students would be able to produce a coherent explanation of the subject even after a few months. Even so, mathematical maturity and an interest in mathematics would likely remain.

With this in mind, such a short math course should contain an introduction to rigor and proof, demonstrating how mathematics is done in the real world. Beyond building mathematical maturity though, it should have content in the form of big ideas. Maybe it would not be possible to communicate those ideas perfectly precisely, but as long as the spirit and the coolness of those ideas is communicated, I consider the course to be a success.

The summer has been entertaining for nonmathematical reasons as well, such as water guns, a war hammer, and a sword named Dragonsbane.

For the remainder of the summer, the plan is hibernation. Observe that penguins live in Antarctica, where it is currently winter, so it is obviously the correct season for hibernation!

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