About Me
I am an undergraduate student at the University of Victoria. My academic interests include graph theory, topology, and many other branches of pure mathematics. I am passionate about education, and believe that my most important task is to learn how to express mathematical ideas clearly and effectively to many different audiences. I love being curious and keeping an open mind. In my (infinite) spare time, I tinker with photography, graphic design, and ideas.If you’ve heard of Erdős Numbers, Erdős-Bacon Numbers, and the fact that Queen lead guitarist Brian May has a PhD, you may have wondered whether Brian May (being connected to both the scientific and entertainment worlds) has a well-defined Erdős-Bacon number. As a matter of fact, he does: here’s how the rock legend is connected to the centres of cinema and academia.
Brian May’s Bacon Number: 3
It turns out that Brian May does have a Bacon Number: the Oracle of Bacon gives him a 2, but the link relies on a concert recording and feels like it’s kind of cheating. Fortunately, there is a more legitimate path of length three, thanks to the guitarist’s credited voice role as “Massed Peasant Chorus/Chamberlain” in The Adventures of Pinnochio. For the record, the links are
Brian May –(The Prince’s Trust Rock Gala)–> Phil Collins –(Balto)–> Kevin Bacon
and
Brian May –(The Adventures of Pinnochio)–> Martin Landau –(Ed Wood)–> Bill Murray –(Wild Things)–> Kevin Bacon
Brian May’s Erdős Number: 7
Thanks to IMDB, the Bacon number was the easy part to find out. The equivalent tool in mathematics is the AMS’ Collaboration Distance tool on MathSciNet. Unfortunately, astrophysics is too far removed from mathematics for the tool to catalogue, so to find Brian May’s Erdős number one has to track down papers manually. The best previous attempt I found was a path of length eight, through a popular science book cowritten by May. However, I managed to find a shorter path, starting with a letter published in Nature:
Brian May –(Nature 240)–> T R Hicks –(The Astrophysical Journal 232)–> J P Phillips –(J. Phys. G 22)–> K Golec-Biernat –(Acta Phys. Polon. B 22)–> Th. W. Ruijgrok –(Phys. A 84)–> C.J. Thompson –(Proc. Nat. Acad. Sci. U.S.A. 55)–> Mark Kac –(Amer. J. Math 62)–> Paul Erdős.
This gives Brian May an Erdős-Bacon number of at most 10, and the smallest known Erdős-Bacon-Sabbath number of 11 (beating Richard Feynman, 14, and Natalie Portman, 13)!
Big numbers are a problem – specifically, a political one. Humans have never been good at coming to grips with the truly astronomical – it has only been recently in our evolution, after all, that we’ve had to tackle any number ending in “illion” – and we usually have to resort to crazy visualizations or a logarithmic scale to make any sense of big numbers. This makes it very difficult for the average taxpayer to put government announcements in context, because what is a government budget but a list of extremely large numbers? That’s one of the reasons that I love the annual Death & Taxes poster: it makes it so much easier to see the big picture. Unfortunately, there’s only a Death & Taxes chart for the United States federal budget, which (as interested as I am in American politics) doesn’t affect me all that much. That’s why I thought I’d do something similar with the British Columbia provincial budget, and get a feel for the orders of magnitude involved.
The BC provincial budget in convenient graphical form!
All figures come from the 2009 estimates document found at the bottom of this page. As in the original Death & Taxes, everything is to scale; that is, the area of each circle is proportional to the money it represents.
Mmmmm… homemade cinnamon buns. They’re as good for your taste buds as they are bad for your diet, so you should make sure you’ve got somebody to share with! Fortunately, finding volunteers to eat these shouldn’t be too hard. This recipe is a modified version of one I found in the Canadian Living Cookbook.
Ingredients
- 1 cup lukewarm water
- 1 pkg instant yeast
- 1/4 cup vegetable oil
- 1 cup milk
- 2 tbsp sugar
- 2 eggs
- 6 cups (ish) all-purpose flour
- 1 cup soft butter
- 2/3 cup brown sugar
- raisins
- cinnamon
- 3 cups icing sugar
- 1/2 cup butter
- 1 tbsp vanilla
- 2 tbsp milk
Directions
- In a large mixing bowl, sprinkle yeast over lukewarm water. Add oil, milk, and sugar, stirring until sugar dissolves. Beat eggs into the mixture.
- Gradually beat in flour, half a cup at a time, until batter becomes thick and smooth. Stir in enough remaining flour until dough is easy to handle.
- Knead dough on a floured board, adding flour when necessary, until dough is smooth, elastic, and no longer sticky.
- Place dough in greased bowl and turn to grease all over. Let dough rise in a warm, dark, draft-free place for an hour or so, until it has doubled in size.
- When the dough has risen, punch it down and split it in half. Roll out each half on a lightly floured board into rectangles about the size of a baking pan.
- Stir together soft butter, brown sugar, and enough cinnamon to make mixture a dark brown. Spread this mixture to cover the dough. Sprinkle raisins over top.
- Starting at the widest end, roll each rectangle into a long, thin cyclinder. Cut each cylinder into eight cinnamon-bun-sized pieces, and place them on a baking sheet.
- Bake in 375° F (190° C) oven for 20 minutes.
- While the buns are in the oven, make the icing. Mix 1/2 cup butter with icing sugar, vanilla and 2 tbsp milk, adding icing sugar and milk as necessary to achieve desired consistency.
- When the buns are ready, take them out of the oven and place them on cooling racks with tinfoil underneath. Place a spoonful of icing on the top of each bun while it is still hot, letting the icing melt and cover the whole bun.
"...for in service I am not."
We’ve been covering Stirling numbers in combinatorics recently, using what Wikipedia tells me is Karamata notation. It’s similar to the notation for binomial coefficients but with different style brackets:
Binomial coefficients and Stirling numbers
Of course, new notation means I had to learn some new LaTeX code! Here’s the solution I came up with, in case anyone else needs to know how to do Stirling numbers in LaTeX.
I just learned a while ago that the amsmath package provides the command \binom{n}{k} for “n choose k”. This syntax isn’t particularly useful for what I needed to do, but I looked \binom up in The LaTeX Companion just in case, and it turns out that it’s a special case of a far more powerful amsmath command.
I’m talking about a six-parameter beast called the generalized fraction command:
\genfrac{leftbracket}{rightbracket}{linethickness}{style}{numerator}{denominator}
\genfrac generates a fraction-like notation and encloses it in brackets given by the first two arguments. Stirling numbers, unlike fractions, don’t have a line between the expressions on the top and bottom, so we have to make it “invisible” by setting the line thickness to zero. Once we’ve done that, we can just give \genfrac the right brackets and we’re good to go!
For example, you can typeset a Stirling number of the first kind using
\genfrac{[}{]}{0pt}{}{n}{k},
and a Stirling number of the second kind with
\genfrac{\{}{\}}{0pt}{}{n}{k}.
Of course, it might be a good idea to define a \newcommand if you use a lot of Stirling numbers in an assignment!
