fun calculations

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The Sunrise Equation

In my quest to watch a sunrise recently, I had to search the web to find out the time before which I needed to get up. Predicting the sunrise is something that I had pondered before. I'm sure numerical simulations are more accurate, but I began deriving a simple formula. Everyone knows the gist of why the Sun rises and sets and why this experience depends on your location on the globe. The answer is that it all depends on the tilt of the Earth's axis.

The relationship between the tropics and the solstices.

The Earth's axis of rotation makes a certain angle with the normal to the plane in which it orbits. This angle of inclination is $ 23.5^{\circ} $. It is not hard to picture how this affects the seasons and why the tropics are offset from the equator by $ 23.5^{\circ} $ as well. I found it much harder to visualize the effect that the inclination has on the length of a day and most people I've talked to simply take it on faith that the Arctic and Antarctic circles are at $ 66.5^{\circ} = 90^{\circ} - 23.5^{\circ} $ latitude.

So now is our chance to overcome this hurdle. Together, you and I will figure out how to calculate the length of a day as a function of time for all latitudes. Hint: it is not a smooth function!

I Didn't Start Believing This Yesterday

I'm finding it hard to believe that it has already been three weeks since I graduated from Queen's. My favourite part of the ceremony by far, was the speech by Emeritus Professor of physics, William McLatchie. This is not just because he mentioned a former student of his, Ted Hsu, the only politician who has ever made me feel thrilled about voting. His speech was unconventional by many standards.

First off, I would expect many graduation speeches to be congratulatory in nature. His was far from it - in fact he said that "mathematics acts as a diode." A much debated claim is that it is easier for the mathematically inclined to follow non-mathematical pursuits than it is for others to do the reverse. But his point was that PhDs who spend their days filling chalk boards with Greek letters - despite their desire to treat non-academics as equals - are regarded by the public as an out-of-touch, nerdy elite. The number of graduands who were on the path to receive a PhD in a quantitative science was rather high, so he felt compelled to tell us what may be a sad truth - that the degrees we would be getting would stigmatize us for the rest of our lives.

Maybe when I have a PhD, no one will want to believe the things I blog about. They might think I'm corrupt enough to put my research before the good of the world. When I try to defend my arguments, they might accuse me of using my academic super-powers to confuse and intimidate. Before that happens, there's something very important that I should mention to you. Even though I am known as quite a stubborn person, I can think of three major topics about which science has convinced me to change my mind:

  1. I am now suspicious of the merrits of recycling paper.
  2. I no longer believe that marijuana is a dangerous drug.
  3. I support nuclear energy.

I want to talk about the last one.

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