Sunday, July 15, 2012

Stream-of-Consciousness Bullets of Getting There

We made it to Australia on Wednesday! It was a long journey. Here are a few stream-of-consciousness bullets about the trip and the past few days:
  • Vinny had never been on a plane before. I was worried that he would not like it. He enjoyed our short flight from Lexington to Dallas, thank goodness. But then I was worried he would not enjoy the flight from Dallas to Brisbane, which is literally the longest flight possible with current commercial aviation technology.
  • I need not have worried. They had an in-flight entertainment system which kept him occupied for the whole flight.
  • I, however, was ready to get off that plane. The jerk in front of me kept his seat reclined the entire flight, which put my in-flight entertainment system so close to my face that it was almost too close to view. Thank goodness they made him sit up during the meals!
  • Speaking of meals, they fed us well. Even during our cross-continental flight from Sydney to Perth.
  • I was really disappointed that, when we went through immigration, customs, and quarantine, I did not see any of my favorite people from "Border Security: Australia's Front Line." I was also disappointed that nobody wanted to see the list of the contents of our bags that we had so painstakingly compiled. But, it was probably for the best, because we had a fairly tight connection.
  • We almost missed our flight to Perth because we almost left Vinny's car booster seat behind. We forgot that we had it checked in as a seventh bag. By the time we figured it out, we had gone through customs and were rechecking our bags for our flight to Perth. Jeff went to the baggage help desk and retrieved it, and he finally got it just in time that we could run through the airport and be the last people to board the flight to Perth, which had fortunately been delayed.
  • Once we arrived, we were met by a friend who is also an American woman living in Perth. She is the friend of a friend at my former workplace (still feels weird to call it that). I had spoken with her a lot over the internet and corresponded with her via email, so it was really nice to meet her in person. She was very friendly and very helpful.
  • On Thursday, we went into Perth to get bus passes and phones. We purchased the bus passes and then we ended up using them to go to a post office where they had some particular phones that were unlocked and could be used on any network and were on clearance. 
  • Yup, we went to the post office to buy phones. Turns out you can buy lots of strange things at the post office. Perhaps the most bizarre was that last week they had a special on sewing machines.
  • We have decided that we are going to try to go without a car for as long as possible. It is doable here. We are staying in temporary housing for 4 weeks, and it is about 1/2 km to the nearest grocery store. It is possible to take the bus to where I work. We are looking for similarly walkable longer-term housing.
  • They use the metric system here. I am still trying to get used to it. I do have some standards though, and I will be spelling the base unit of length as "meter" until the day I die.
  • On Friday, we got a bank account and I had to sign some papers for my soon-to-be workplace. Jeff and Vinny got to meet some of my future colleagues and see where I will be working.
  • On Saturday, our American friend took us to the biggest farmers market I have ever seen. It was amazing, especially considering it is winter right now in Australia. We bought a whole chicken, some potatoes, carrots, mandarin oranges and apples, and a liter of Gurnsey milk. We cooked the chicken and potatoes for dinner, and flavored the chicken with salt and pepper and a lemon we had picked in a nearby yard. The lemon was huge -- so big I could only use half of it on the chicken.
  • Speaking of winter, I am having trouble wrapping my head around the fact that it is winter. To me, it feels like we must be in the mountains. That explains the cool weather (because it is really not winter weather from my perspective). Although the lemon tree, and the gigantic aloe bush, and all the other strange vegetation contradict this theory.
  • I start work on Monday. I am looking forward to it.

Tuesday, July 03, 2012

Adventures in Temperature Conversions

You may remember the complicated Fahrenheit-to-Celsius and Celsius-to-Fahrenheit conversion formulas. Or you may not remember them, but you may remember the fact that they are complicated, and involve 5/9 and 9/5, and adding or subtracting 32. But do you add (or is it subtract?) first, and then multiply, or do you multiply first, and by which factor?

Worry no longer, my friends! There is a much easier way to do it. The only formula you will need is the following:
T1 = (T2+40)*factor - 40.
The end.

This formula works for both temperature scales (so {T1,T2} = {F,C} or {C,F}). The only thing you need to remember is whether factor is 5/9 or 9/5. But that is not so hard: there are more degrees between freezing and boiling in Fahrenheit than Celsius, so when you convert to Fahrenheit, you need to use the bigger number, 9/5. Likewise, when converting to Celsius, use 5/9.

Does it really work? Yes! Let's do some examples.

Body temperature is 37 C or 98.6 F. Can we convert to those numbers? Let's start with C to F:
F = (C+40)*9/5 - 40
F = (37+40)*9/5 - 40 = 77*9/5 - 40 = 138.6 - 40 = 98.6
Now what about F to C?
C = (F+40)*5/9 - 40 
C = (98.6+40)*5/9 - 40 = 138.6*5/9 - 40 = 77 - 40 = 37
You can derive the traditional formulas for temperature conversion from this simple one.
F = (C+40)*9/5 - 40 = 9/5*C + 40*9/5 - 40 = 9/5*C + 72 - 40 = 9/5*C + 32
C = (F+40)*5/9 - 40 = 5/9*(F+40 - 9/5*40) = 5/9*(F + 40 - 72) = 5/9*(F - 32)
As easy as this formula is, it's still non-trivial to do in your head. So my sister Rachel told me an easy thing to remember about Celsius temperature ranges when it comes to the weather:

  • 40+ C: extremely hot (=104+ F)
  • 30-39 C: very hot (=86-102 F)
  • 20-29 C: comfortable-hot (=68-84 F)
  • 10-19 C: cool-comfortable (=50-66 F)
  • 0-10 C: chilly (=32-42 F)
So the ideal you'd be most comfortable in is the range around 20-25 Celsius (68-77 F). From there you can see how much the temperature deviates from the ideal. (In Perth, once every couple of years it dips down to freezing, so I did not go any lower on the scale.)

Sunday, July 01, 2012

Adventures in Fibonacci Numbers

You may remember the Fibonacci numbers from math class. The Fibonacci sequence of numbers is easy to generate: begin with 0, 1. Then add the two previous numbers to get the next number in the sequence:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144...
If you take the ratio of consecutive numbers in the sequence, you can see an interesting pattern:
0, 1, 0.5, 0.667, 0.6, 0.625, 0.615, 0.619, 0.6176, 0.61818, 0.617977, 0.618056...
Graphing these numbers, we can see that they seem to be honing in to one number -- increasingly accurate lower and upper bounds to a number that turns out to be roughly 0.61803, or more exactly 2/(sqrt(5)+1), the reciprocal of the Golden Ratio.

(In the above graph, I cut out the first few ratios so we could see the trend better.)

There are a lot of cool applications to for the Fibonacci sequence. It is often found in nature -- for example, the arrangement of seeds in a sunflower head, or the unfurling of a fern. There are also computer science data storage techniques, such as Fibonacci heap, that are derived from the sequence.

But a really cool use of Fibonacci numbers that I learned recently is the conversion between miles and kilometers. As it turns out, the ratio of miles to kilometers (0.621371192 mi/km) is pretty close to the ratio to which sequential Fibonacci numbers converge (0.61803), so we can use the sequence of Fibonacci numbers to roughly convert from miles to kilometers and vice versa. If we want to convert 3 miles to kilometers, for example, we simply take the next number in the Fibonacci sequence, so 3 miles is about 5 kilometers. (Doing the actual math, it's 4.828, which is pretty close.) Similarly, if we want to convert 13 kilometers to miles, then we take the previous number in the Fibonacci sequence, so 13 km is about 8 miles. (Again, doing the actual math, we obtain 8.078, so not bad!)

If you have a number that is not in the Fibonacci sequence, you can simply break it down into two Fibonacci numbers (there's a theorem that says you can do that for any integer!), and do the conversion on those two numbers and add the results back together. So, if you want to know what 60 miles is in kilometers, you break down 60 into 5 + 55, and convert them both to kilometers, so 8 + 89, to obtain an answer of 97 km. The actual answer is 96.56 km, so not too bad!

I plan to use this handy conversion factor in Australia to help me transition into understanding distance in kilometers. But also because it is just about the coolest thing I have seen in a long time!