In the beginning

Happy Pi Day, everyone! It’s March 14 (or 3-14), the day to celebrate everybody’s favorite irrational number. You can check out my post from last year to learn all about pi and Pi Day.

I will, unfortunately, not be celebrating Pi Day by making a pie, as is customary. I just don’t have the time this year. It’s crunch time, as we all know, and I’m rushing to get everything done.

Yesterday I took a big bite out of the introduction. It’s amazing to me how difficult it often is to write the first sentence of anything. I stared at my intro for a long time, even typing out later paragraphs of it months ago, but I had no clue how to begin. There were about fifteen different approaches I could take to introduce my project, but I didn’t like any of them. Finally, I sat down with my advisor, and we talked about the big picture of using perfect sine waves as a “ruler” for time and distance measurements. The closer your sine wave is to perfect, the more accurate your ruler is (that is, the “one inch” mark is definite, not kind of fuzzy so you don’t know where in the width of the fuzz the actual one inch mark is). Noise makes fuzz in the the zero crossings of a sine wave, thus giving some uncertainty about the exact duration of “one second.” Since making a truly perfect sine wave is impossible, the whole point of our research is making sine waves that have as little fuzz around the zero crossing as possible, making for a more accurate measurement.

That’s the route I finally decided to take to introduce my project, and it flowed quite naturally out of that. I stayed extra late last night to make some progress on that chapter, and now I have just one more section to write and I should be done with this draft. All that will leave for completely original writing is the conclusion, which should be straightforward to write given the arguments that have been presented in the rest of the paper. I would say that completely finishing the initial writing stage by the end of the week is totally on the radar.

I still have lots of revisions to do (once my advisor gives me back his comments on all the chapters he now has) and still that stupid, lingering data problem (which is slowly working itself out, but, unfortunately, not to a clean and tidy end). However, I really hope that the majority of changes will not require lots of onerous effort. Then it can go quickly, like an avalanche down to the final end. I know there will still be hiccups, but I’ve got my eye on the prize now, and I can just taste the freedom coming my way.

So, today I hope to finish the introduction and get started on the conclusion. Then I’ll go back to revisions I got previously and work on those while I wait for more feedback. Wednesdays haven’t been that motivating or productive the last couple of weeks, but I’m ready to buck the trend today!

 

Happy Pi Day!

Happy Pi Day everyone! In month-day date format, today is 3-14. These are the first three digits of the mathematical constant π. I thought we’d celebrate with a little history and fun facts.

Yes, I do own a book about pi. And no, it’s not the one about that Indian boy and the boat.

To fifty digits, π=3.14159265358979323846264338327950288419716939937510.

Pi is the ratio of a circle’s circumference (distance around the circle) to its diameter (distance straight across the circle). It is an irrational number, never repeating and never ending, meaning that no matter how many digits one might calculate, there are always more without discernible pattern. Never fear, however—eleven digits will give you a circle the size of the earth with an error of less than a millimeter, and 39 digits will yield a circle fitting inside the observable universe accurate to the size of a hydrogen atom. I guess that’s pretty good (we still measure time more precisely, though!).

Many ancient civilizations, including the Egyptians, Babylonians, Indians, and Hebrews, either understood the relationship between these parts of a circle or had at least a rough calculation of the ratio. The Greek scholar Archimedes first rigorously estimated the value. The Chinese later produced the most accurate value of pi that would prevail until sometime around the 1400’s. Today, with the advent of computers and modern algorithms based on converging series and Fourier transforms, one can calculate multiple trillions of decimal places even on a personal computer. However, since we previously discussed how this is not necessary, we conclude that these activities are merely exercises in nerdy pride.

The ratio 22/7 is a common approximation of pi; therefore, Pi Approximation Day is celebrated on 22 July (day-month date format). On Pi Day, the Pi minute can be celebrated at 1:59:26 a.m. as well as 1:59:26 p.m. if one uses the 12-hour clock convention. That gives the 7-decimal place value of 3.1415926. In the year 2015, Pi Day will be 3-14-15; thus, the pi second at 9:26:54 a.m. (and p.m.) yields the ten-digit value of 3.141592654. So please don’t forget to celebrate Pi Day four years from now; it will be eπc.

Thanks to the Wikipedia articles on Pi and Pi Day for info.