Designing a flyswatter is an interesting exercise in 
optimization.
You want it have enough holes so that it can quickly achieve swatting speed, but you don’t want it to have so many holes as to substantially decrease the chance of actually making contact with the pest.
I wonder if there is an industry standard for a flyswatter’s empty-space-to-surface-area ratio.
According to a recent study the default rates for mortgages over one million dollars is nearly twice as high as the default rate for mortgages under one millions dollars (14.3% to 8.3%). A default on a mortgage essentially means that the home-owner stops making mortgage payments and the bank takes possession of the home.
There are a lot of interesting mathematical, sociological, and perhaps ethical questions here, but I wanted to point out that although the above probabilities are interesting, the number and total value of the mortgages in question are probably more relevant data to consider.
For example, if only 1/10 of all mortgages are over a million dollars, then this statistic might not be that important; on the other hand, if a good number of defaults are way over a million dollars, than this statistic isn’t telling the real story either, but in a different way.
As an aside, renting vs. owning is a general and interesting mathematical question to explore in a variety of different contexts.
Paul the octopus must be enjoying his 15 minutes of fame for correctly predicting the outcomes of eight World Cup matches in a row. In fact, a stamp in his honor is currently available at the Shanghai World Expo. This must be a welcome relief from the death threats that followed his [ultimately accurate] prediction of Spain over Germany.
Assuming that the outcome of every match was equally likely (what if you don’t?), then Paul had a 1/256 chance ( that is, (1/2)^8 ) of nailing all eight predictions. That’s roughly a .4% chance, on the order of getting dealt a straight in a five-card poker hand, or rolling a six three times in a row on a fair die. Or, if you prefer, exactly equal to the likelihood of flipping a coin and getting Tails (Arms?) eight times in a row.
Apparently octopi have short lifespans, so it doesn’t look like Paul will be around in 2014 to put his record on the line. At least he’ll go out on top.
The NYT’s soccer blog (I can start calling it soccer again, right?) has a nice selection of tools to analyze the stats from yesterday’s World Cup Final:
http://goal.blogs.nytimes.com/2010/07/11/world-cup-live-netherlands-vs-spain/
The default is the “Heat Map”, which attempts to show the region of play minute-by-minute. That’s not nearly as interesting to me as the the “Passes” tab, which appears to detail each possession with an undirected graph, connecting two players with an edge if a pass occured between them (How do we know who passed to whom? What if two players passed back-and-forth to each other? Why not indicate turnovers in this manner?). Using a graph like this could certainly help an analyst determine the worth of a player on the field.
There’s also a sidebar that shows various stats from the game. For example, you can see that the seven players with the highest number of “Touches”, and the top eight in “Passes”, were all Spaniards. This supports the general description of their style of play (a lot of passing and waiting, I guess). After looking at those stats for a bit, I couldn’t help but laugh when I pulled up the list for “Goals”.
There’s a lot of statistical analysis here for a game that was tied at zero for two hours.
I saw a movie last night at the Brooklyn Academy of Music (BAM). BAM shows a few movies every day–some new and some old–but it’s not their primary means of generating revenue. Presumably that comes from local and national funding, private donations, and the like.
So how much money do they make showing movies? Well, last night’s movie was sold out, making it easy to estimate how many tickets were sold: 11 rows x 14 seats per row = 154 seats. The rows in the back might have had an extra seat, so let’s call it 160. At $12 a ticket, that’s $1920 in ticket sales. Concessions are a big winner for movie theaters–a quick search suggests that a $3 concession per capita rate is appropriate, so let’s assume that the theater generates an additional $3 X 160 = $480 in concessions. So that’s $2400 in total revenue for what is probably the busiest showing of the week (Saturday night).
What are BAM’s costs? Well, they have to pay to show the movie (I don’t know if this is a flat fee, a per-showing fee, a per-viewer fee)’; they must pay employees (sales, ushers, concessions, security, projectionists, janitors); and they probably lose a cut to on-line ticket brokers. Doesn’t seem like a high rate-of-return to me, especially when they only show a couple of movies per day.
One thing is for sure: there are people out there who are very happy that they are still generating revenue by selling the rights to show a 50-year-old movie (“Charade”) in theaters. That’s the business to be in.