Dork Scratchings

 Photo taken in the Outer Hebrides by my brother-in-law (The doctor one, not the Flat Earth one) This photo was taken a few days ago by my brother-in-law Alex from the Outer Hebrides where he's off galavanting at the moment. You can clearly see that half the ship is missing indicating either a) it's sinking b) the Earth is round Going with (b) for the time being we can actually come up with a pretty good guesstimate for the size of the Earth just from this picture. Let's guess that the ship is 10km away. (That's not likely to be accurate but it's certainly more than 1km - the width of Lake Windermere - and less than 100km - the distance from Portsmouth to Le Havre). So $l=10000$. Now let's assume that the bottom 10m of the ship is missing from view (again, not likely to be accurate but good enough for an order of magnitude calculation). So $h=10$. Now chuck it into this equation which is easily worked out with a bit of trig $$ r=\frac{l^2}{2h} $$ and, hey presto...

  Visual metaphor and pun Since my previous  post I've been thinking a bit more about Rubik's Cubes.  I have been wondering what is the simplest way to represent their state mathematically, and by extension programatically. Configurations of the cube clearly form a group, so I set myself the goal of creating objects in python which would represent individual configurations and which could be multiplied together to form new objects.  For example, $I$ would represent an unscrambled cube, $L$ a cube obtained from $I$ by moving the left face clockwise, $U$ a cube obtained from $I$ by moving the upper face clockwise and $L*U$ the cube obtained by rotating the left face first and then the upper face. The question is: what is the most elegant representation for each of these objects?  I was initially drawn by the idea of labelling the stickers (other than the centre face ones) 1 to 48 and representing each object as a different permutation.  This makes multiplica...